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Evaluation of saturation dose in spatial distributions of color centers generated by 18 MeV proton beams in lithium fluoride
Nuclear Inst. and Methods in Physics Research B 464 (2020) 100–105
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Nuclear Inst. and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Evaluation of saturation dose in spatial distributions of color centers generated by 18 MeV proton beams in lithium fluoride
T
E. Nichelattia, , M. Piccininib, C. Ronsivalleb, L. Picardib, M.A. Vincentib, R.M. Monterealib ⁎
a b
ENEA C.R. Casaccia, Fusion and Technologies for Safety and Security Dept., Via Anguillarese 301, 00123 S. Maria di Galeria, Rome, Italy ENEA C.R. Frascati, Fusion and Technologies for Safety and Security Dept., Via E. Fermi 45, 00044 Frascati, Rome, Italy
ARTICLE INFO
ABSTRACT
Keywords: Radiation detectors Protons Lithium fluoride Dose map Bragg curve Color centers Photoluminescence
The paper concerns the analysis of spatial distributions of visible photoluminescence of optically active F2 and F+3 color centers created in lithium fluoride crystals by irradiation with proton beams. Spectrally integrated photoluminescent maps are detected in a fluorescence microscope and numerically elaborated to gather pieces of information regarding both the beam characteristics and the material response. A method based on two independent measurements (Bragg curve and beam transversal map) is developed to evaluate the saturation dose defined as the value above which the photoluminescence intensity begins saturating up to an asymptotic maximum. The paper describes the procedure and demonstrates its application to the experimental case of LiF crystals irradiated by a proton beam of 18 MeV nominal energy.
1. Introduction The interaction of ionizing radiation of various kinds—X-rays, γrays, UV light, accelerated ions and electrons—with the crystal lattice of lithium fluoride (LiF), either bulk or thin film, causes the formation of point defects, known as color centers (CCs), due to the release of energy in the material by the impinging radiation [1]. Some of these CCs, the F2 and F+3 defects (two electrons bound to two and three close anion vacancies, respectively) are optically active: they emit Stokesshifted photons in the visible (red and green spectral regions, respectively) when optically pumped at blue wavelengths corresponding to the M band, peaked at 450 nm, made of the two overlapping bands of F2 and F+3 CCs [2,3]. Solid-state imaging detectors for several types of ionizing radiation based on photoluminescence (PL) from CCs in LiF have been receiving in the past years more and more interest thanks to their high intrinsic spatial resolution, high dynamic range and good linearity across several orders of magnitude of the absorbed dose [4–17]. Since the CC concentration in the material is point-by-point related to the amount of absorbed energy, the intensity spatial distribution of the radiation that impinges on a LiF-based detector can be retrieved by mapping and analyzing the PL intensity by means of a properly equipped optical fluorescence microscope. The easiness of handling, excellent stability of CCs in daylight, and immediate availability for post-irradiation inspection make radiation detectors based on PL from CCs in LiF a
⁎
promising opportunity for radiation imaging purposes. Moving from the detection of CCs to their generation, it must be emphasized that accelerated hadrons are being more and more used in oncological radiotherapy [18–23]. Their penetration depth is mainly determined by their mass and energy, together with the characteristics of the material being irradiated. Differently from X-rays, accelerated hadrons release most of their energy in the final part of their path. Such a feature is very desirable in radiotherapy, because it allows to confine the deposited energy mostly within the targeted tumoral mass, while affecting the neighboring healthy tissues much less than X-rays. The depth profile of the energy that mono-energetic hadrons deposit in the material is quantitatively described by a typical curve, known as Bragg curve [24]: this curve features a slowly increasing profile with depth, followed by a sharp increase in correspondence of the so-called Bragg peak, wherein most of the deposited energy lies. Our research team has been successfully using LiF-based detectors for proton-beam diagnostics [11,13–15,25–27] within the TOP-IMPLART project for protontherapy [28]. In this project, the structure of the proton accelerator consists of a series of accelerating modules that are being gradually added to a commercial 7 MeV proton linear accelerator model PL7 by AccSys-Hitachi, which works as a low-energy injector. Measurements and tests are envisaged for each added module as part of the machine commissioning. In the present paper, our attention is more directed on the characterization of the material PL response to 18 MeV proton irradiation, in particular on a quantitative estimation of
Corresponding author. E-mail address: [email protected] (E. Nichelatti).
https://doi.org/10.1016/j.nimb.2019.12.012 Received 24 October 2019; Received in revised form 10 December 2019; Accepted 15 December 2019 0168-583X/ © 2019 Elsevier B.V. All rights reserved.
Nuclear Inst. and Methods in Physics Research B 464 (2020) 100–105
E. Nichelatti, et al.
the dose that causes saturation of the PL emitted by optically active CCs in LiF. According to a mathematical model that describes the PL intensity emitted by CCs as a function of the absorbed dose [14], a parameter called saturation dose is enough to quantify such saturation characteristics of the material. It is well known that large aggregates of F centers and macrodefects can be also created above a critical concentration and at irradiation temperatures where the diffusion of single point defects is not negligible [29,30]. Although the coloration of LiF crystals by means of ion irradiation has been the subject of intensive studies by several groups since the 70’s of the past century [29–32] (and references therein) for different ion species, ion doses and annealing conditions, and even though progress has been made on the topic both experimentally and theoretically [29,33], it is still difficult to quantitatively correlate the PL behavior with the defect concentrations as derived from optical absorption measurements [34]. One of the crucial problems concerning irradiated LiF crystals is the coexistence of several kinds of aggregate defects with often overlapping absorption bands, which makes it difficult to clearly isolate and measure the actual contributions due to the individual centers. In this regard, PL measurements are more sensitive than the absorption ones in investigating the presence of visible-emitting electronic defects and optical spectroscopy is a useful tool to separate the distinct contributions of F2 and F+3 CCs [34,35], but a fully quantitative description is still missing, especially at high irradiation doses. The purpose of the present investigation is to demonstrate how by putting together the pieces of information obtained from the analysis of specific kinds of PL intensity maps, one can estimate the saturation dose in a consistent way. The paper is organized as follows: after a description in Section 2 of the proton irradiation parameters and PL imaging setup, the theoretical method developed to evaluate the saturation dose by comparing elaborations of Bragg curves and dose maps is described in Section 3. Its application to LiF crystals irradiated by 18 MeV protons is reported in Section 4. Reliability and limits of the approach are discussed in Section 5. Finally, the obtained results are summarized in Section 6.
The nominal proton energy at the accelerator exit was 18 MeV. The beam current was 20 µA , the pulse repetition rate was 10 Hz, the charge brought by each pulse was 64 pC , and the pulse duration was 3.2 µs . The distance between the accelerator 50 μm-thick Ti exit window and the LiF crystals was 50 mm . Each irradiation consisted of a total of 2,400 pulses, which corresponds to a spatially-averaged dose absorbed at the surface of LiF (within the beam cross section) of about 1.8 × 10 4 Gy , as calculated from accelerator parameters—the uncertainty we ascribe to this value is ± 3%. The energy loss and straggling suffered by the protons for the propagation in air from the Ti window to the LiF crystals were estimated by elaborating in Matlab [36] a SRIM (version 2013.00) [37,38] simulation of 18 MeV proton propagation in air (89,999 protons, quick calculation algorithm). The resulting values were: mean energy loss of 150 keV and standard deviation of the energy distribution (straggling) of 21 keV . After the irradiations, the visible spectrally integrated PL images emitted by the spatial distributions of F2 and F+3 CCs generated in LiF due to the proton beam interaction with the lattice were acquired at 2× magnification in a Nikon Eclipse 80-i fluorescence microscope equipped with a Hg lamp and an Andor Neo s-CMOS camera [26]. To perform Bragg curve analysis as in [15], a PL-intensity depth profile was extracted from the digital image acquired after the 1D-setup irradiation by averaging along the x-direction the intensities of the pixels contained in rectangle R2 of Fig. 1. All the numerical elaborations appearing in this paper were performed in Matlab with specifically written codes. 3. Theory Under the simplifying hypothesis that the intensity of PL emitted by CCs in LiF is point-by-point proportional to their concentration, the relationship existing between the PL intensity I and the absorbed dose D is assumed to be ruled by the formula [14]
I (D ) = I
2. Materials and methods
1
exp
D Dsat
,
(1)
where I is the asymptotic maximum value that the PL intensity would assume for infinitely large dose, and Dsat , the saturation dose, is a parameter representing the dose above which the saturation of I becomes evident. The above formula represents an approximately linear growth of I with D, followed by saturation for high values of D. For the concentrations of complex centers in LiF, like the F2 and F+3 defects, other investigations—regarding generation of CCs in LiF by ion irradiation—report more elaborated models that account for the aggregation mechanisms of F centers [31,33]. It is not clear yet how to quantitatively correlate the PL intensity behavior with the defect concentrations as derived from optical absorption measurements, on which those studies rely. Best fits of available experimental data, such as those reported in [25,39–41] for 3 and 7 MeV protons, show that Eq. (1) is suitable to describe the behavior of spectrally integrated PL vs. dose (or absorbed energy) from CCs generated by low-energy protons in LiF. On the other hand, our attempts to best fit the same data with more elaborated models led to less satisfying results. We assume the same conclusion in favor of Eq. (1) to hold also for the present case of 18 MeV protons. The comparison of the PL-intensity spatial distributions obtained in the 2D-setup and 1D-setup (Fig. 1) allows finding a common value of the saturation dose Dsat , as explained in the following.
The samples were two polished 10 × 10 × 1 mm3 LiF crystals, commercially available by Macrooptica Ltd. They were irradiated at normal incidence—one on its 10 × 10 mm2 face (‘2D-setup’), the other on its 10 × 1 mm2 side face (‘1D-setup’), see Fig. 1—in air at room temperature with an accelerated proton beam generated by the linear accelerator that is being developed at ENEA Frascati for the TOP-IMPLART project [28]. The irradiation parameters were the same for both setups.
Fig. 1. Scheme of the setups for the proton irradiations of LiF crystals. Left side: 2D-setup for dose mapping reconstruction. Right side: 1D-setup for Bragg curve analysis. In the 1D-setup, rectangle R2 indicates the area considered to extract the PL-intensity depth profile from the PL image detected at the fluorescence microscope, while rectangle R1 is the corresponding area on the thin side of the crystal within which the entrance dose Din is evaluated (see Section 3.2). The same rectangle R1 is shown also in the 2D-setup, where it is centered around the peak of the PL-intensity distribution; the mean dose at the surface within R1 in the 2D-setup is assumed to be equal to that within R1 in the 1D-setup, see Section 3.3.
3.1. 2D dose map Indicating with (x , y ) the spatial coordinates of the plane coinciding with the proton-irradiated 10 × 10 mm2 face of the LiF crystal in the 2Dsetup—see Fig. 1—the map of absorbed dose, D (x , y ) , is obtained by 101
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properly elaborating the distribution of PL intensity I (x , y ) that is emitted by the optically-active CCs in the material [14,26]. If the proton beam fluence were low enough, one could consider I to be approximately proportional to D in every point of the distribution, but for higher fluences, as those considered in the present paper, saturation phenomena have to be taken into account by using Eq. (1). Therefore, the dose map is calculated from the PL intensity distribution by inverting Eq. (1),
D x, y =
Dsat ln 1
I (x , y ) . I
at the value found by the best fit, Dsat must become larger (smaller) if Din is increased (decreased). To apply the procedure of [15], LET curves LE, E (z ) were simulated in SRIM at several energies E and energy spreads E —the values of these parameters were tentatively chosen to span ranges that included the sought actual values and to be dense enough for calculating LET curves at intermediate (E , E ) points by linear interpolation. These LE, E (z ) were later processed by means of Matlab, according to what follows. After calculating the related dose-depth profiles DE, E (z ) = LE, E (z )/ —where is the proton beam fluence at the material entrance point and is the material density—corresponding PL-intensity profiles IE, E (z ) were obtained from Eq. (1) for a set value of the fit parameter R Din / Dsat , from which the argument of the exponential function is calculated [15]. These IE, E (z ) profiles were regarded to as elements of a lookup table, so that test PL-intensity profiles with desired intermediate energies and energy spreads could be calculated by linear interpolation; eventually, a least-square optimization allowed finding the best fitting PL-intensity by varying three fit parameters: energy, energy spread, and R [15].
(2)
In order to successfully perform such an inversion, the values of Dsat and I need to be known. Regarding Dsat , it is going to be treated as an adjustable input parameter, as later discussed in Section 4. The intensity I (x , y ) that is detected at the microscope is due to CCs found at various depths in the LiF crystal. This fact means that the detected I (x , y ) can be considered to be the z-average of a more general I (x , y, z ) volume distribution. Assuming the mean absorbed dose D over the irradiated volume V to be experimentally known, one can integrate Eq. (2), obtaining
D =
Dsat S
S
ln 1
I (x , y ) dx dy , I
3.3. Saturation dose estimation
(3)
In the previous Sections 3.1 and 3.2, the saturation dose Dsat was linked to two other quantities: Dmax for the analysis of dose maps in the 2D-setup, and Din for the analysis of Bragg curves in the 1D-setup. It has been pointed out how the variations of the Dsat value are driven by those of Dmax and Din with opposite behaviors: while Dsat increases (decreases) together with Din , it decreases (increases) for increasing (decreasing) Dmax . Because Dsat should be a characteristic parameter of the material, suitable values of Dmax and Din should in principle exist to which a physically consistent value of Dsat corresponds. The above conclusion suggests an experimental approach to evaluate Dsat . If the irradiations in the 2D-setup and 1D-setup are made under the same experimental conditions (proton energy, fluence, etc.), and if the geometry of the 1D-setup is such that rectangle R1 coincides with the most intense part of the proton beam (see Fig. 1), then Din should be equal to Dmax —or approximately equal, if one considers (a) that rectangle R1 is likely to include also doses that are slightly lower than Dmax , and (b) that D (x , y ) is a z-average of the actual volume distribution of dose. Therefore, if Din and Dmax are both increased or decreased, Dsat will change in opposite directions depending on which type of analysis is being performed, either dose map calculation or Bragg curve best fit. As a consequence, defining Dsat,2D {Dsat ; from dose map} and Dsat,1D {Dsat ; from Bragg curve} , smaller values of Dsat,1D should correspond to larger values of Dsat,2D , and vice versa. Hence, a common value of Dsat,2D and Dsat,1D should exist that is compatible with both dose map analysis and Bragg best fit; this value is assumed to be the most plausible one for Dsat .
where the irradiated volume V is formed by a suitable area S in the plane Oxy with thickness h = 1 mm along z. In the surface integral, the further simplifying assumption that the integrand function approximates the z-average of ln[1 I (x , y, z )/ I ] is made. (It should be noticed that, for the proton energy considered in this paper, 18 MeV, the Bragg peak is found in LiF at a depth of 1.6 mm , that is well beyond the thickness of the LiF crystal.) By numerically solving Eq. (3), the value of the unknown I can be determined and used in Eq. (2) to finally obtain D (x , y ) . For what above said, also D (x , y ) has to be understood as an approximate z-average of the actual volume distribution of dose. Due to the shape of the function ln(1 t ) , that monotonically grows with t (0 t < 1), the solution I of Eq. (3) generally depends on Dsat in the following way: for a certain D , to larger (smaller) values of Dsat , larger (smaller) values of I correspond to obtain a smaller (larger) I (x , y )/ I ] dx dy . Since also the t-derivative of ln(1 t ) S ln[1 monotonically grows with t, the largest-valued parts of ln[1 I (x , y )/ I ] change more than its surface-average, thus are more affected than the latter by changes in Dsat . It can be concluded that, according to Eq. (2), the largest-valued portions of D (x , y ) —in particular, its maximum Dmax —should become smaller if Dsat becomes larger, and vice versa, for the right member of Eq. (3) to keep being equal to the given D . 3.2. 1D Bragg curve
4. Results
An experimental evaluation of the Bragg curve of protons in LiF can be obtained by elaborating a thin slice—rectangle R2 in Fig. 1—of the PL image that is detected on the 10 × 10 mm2 face of the crystal after irradiation in the 1D-setup. Such an approach practically corresponds to analyzing a mono-dimensional I (z ) PL-intensity profile, where z is the depth coordinate, with z = 0 at the air-LiF interface and z > 0 inside the material. The I (z ) profile is obtained by averaging over x the intensities of the pixels found within rectangle R2. This kind of analysis was the subject of recent publications by our research team, both in presence [15] and in absence [27,42] of CC saturation. In the former case, we demonstrated for 7 MeV protons how a suitable best fit leads to the full recovery of the proton Bragg curve in LiF, and that the ratio R Din / Dsat of the entrance dose Din —that is, the dose absorbed by LiF within rectangle R1 (Fig. 1, right side)—to the saturation dose Dsat can be evaluated from the best fit, so that Dsat can be estimated from R provided Din is known [15]. To keep R unchanged
For irradiation of LiF bulk with 18 MeV protons, a SRIM simulation (99,999 protons, quick calculation algorithm) showed a nearly linear increase of the linear energy transfer (LET) across the crystal 1 mm thickness: approximately from 6 eV/nm to 9 eV/nm . Therefore, an average LET of about 7.5 eV/nm is expected within the crystal in the 2Dsetup, a value that is 25% larger than the LET at the crystal surface. Consistently, by using the known average dose 1.8 × 10 4 Gy absorbed at the LiF crystal surface in the 2D-setup, a 25% higher average absorbed dose within the crystal volume, D = 2.25 × 10 4 Gy , is expected. Taking into account this value for the calculation of I by means of Eq. (3)—recalling that the I (x , y ) therein appearing represents an average along z of the PL contributions from various depths in the crystal—the procedure to find a reliable value of Dsat from our elaborations was the following. 102
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Table 1 Values of the 2D and 1D elaborations as obtained by varying Dsat,2D .
Fig. 2. Elaboration of the PL intensity depth profile of a LiF crystal irradiated with 18 MeV protons in the 1D-setup. Left figure: PL intensity map detected at the fluorescence microscope due to F2 and F+3 CCs generated by the irradiation; rectangle R2 (see Fig. 1)—whose x-width corresponds to 30 pixels of 3.26 μm size—frames the area from which the PL intensity profile along z was obtained by averaging the pixel intensities in the x direction. Right figure: obtained PL intensity depth profile (dots) and its best fit (solid line), for which the approach explained in [15] was applied; the dose z-profile, calculated from the SRIM simulated LET curve, is also shown (dashed line).
1. The ratio R = Din / Dsat is found from the best fit of the Bragg curve, as explained in [15]. 2. A test value of Dsat,2D is chosen. The unknown I is calculated by numerically solving Eq. (3). The obtained I , together with Dsat,2D, is inserted into Eq. (2) to retrieve the dose map D (x , y ) . The average Dmax of the most intense part of D (x , y ) , coincident with the small rectangle R1 (Fig. 1, left side) is then calculated, its value being close to Dmax and more accurate to apply the approach explained in Section 3.3. 3. Because of the assumption of a 25% higher average dose within the crystal than at its surface, Din is set equal to the value of Dmax diminished by 25%; Din is then used to evaluate Dsat,1D from the known ratio R, by applying Dsat,1D = Din /R . 4. The so obtained Dsat,1D is compared with the test Dsat,2D.
Dsat,2D (105 Gy)
Dmax (10 4 Gy)
Din (10 4 Gy)
Dsat,1D (105 Gy)
1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35
9.246 9.146 9.059 8.981 8.912 8.850 8.794 8.743
7.397 7.317 7.247 7.185 7.130 7.080 7.035 6.995
1.209 1.196 1.184 1.174 1.165 1.157 1.150 1.143
1.17
8.953 ± 0.095
± ± ± ± ± ± ± ±
0.106 0.102 0.099 0.096 0.093 0.091 0.089 0.087
± ± ± ± ± ± ± ±
0.085 0.082 0.079 0.077 0.075 0.073 0.071 0.070
7.162 ± 0.076
± ± ± ± ± ± ± ±
0.021 0.021 0.020 0.020 0.019 0.019 0.019 0.018
1.171 ± 0.020
Fig. 3. Dependence of the saturation dose estimated from the Bragg curve analysis, Dsat,1D , on the same quantity estimated from the dose map analysis, Dsat,2D . The intersection with the quadrant bisector (dashed line), in which Dsat,1D = Dsat,2D , is represented by an empty circle. The confidence bars correspond to 95% probability.
Dsat = (1.171 ± 0.020) × 105 Gy . Using this value, a definitive dose map could be obtained from the PL intensity map detected at the fluorescence microscope; both of these maps are shown in Fig. 4.
The above procedure has to be iterated from step 2 to step 4 by properly changing Dsat,2D , until matching values of Dsat,1D and Dsat,2D are obtained. Regarding step 1, the depth profile of the PL intensity was best fitted by applying the approach explained in [15]. Fig. 2 shows the PL intensity map from which the depth profile—also shown together with its best fitting curve—was extracted as an x-average of the pixelintensity values inside rectangle R2. The value of the ratio of input dose to saturation dose for the Bragg curve analysis resulted to be R = 0.6119 ± 0.0037 . Other meaningful parameters were provided by the best fit, as in [15]: mean proton energy, E = (18.24 ± 0.05) MeV ; standard deviation of the proton energy distribution, E = (143 ± 5) keV ; ratio of the dose DBP at the Bragg peak to the saturation dose, DBP /Dsat = 3.13 ± 0.30 . At step 2, the initial value chosen for Dsat,2D was 1.00 × 105 Gy . Because the Dsat,1D resulting from step 3 was higher than this value, Dsat,2D was incrementally increased, obtaining in this way several values of Dsat,1D that are listed in Table 1 and plotted in Fig. 3. In Table 1, the third column was calculated by decreasing by 25% the second column values to estimate the surface dose Din for Bragg curve analysis. It can be noticed how Dsat,1D and Dsat,2D move in opposite directions, as expected by our reasoning in Section 3.3; the intersection point between 1.15 × 105 Gy and 1.20 × 105 Gy was eventually found and the result is reported in the bottom row of Table 1. The same intersection point is drawn in Fig. 3 as an empty circle, together with a confidence bar which represents the uncertainty in the determination of its value with 95% probability. According to the results of this comparative analysis, it can be concluded that the most reliable value for the saturation dose in LiF (18.24 ± 0.05) MeV bulk irradiated with protons is
5. Discussion Although the procedure to evaluate the Dsat for CCs in LiF crystals worked as expected when applied to the considered experimental case of 18 MeV protons, it is worth clarifying some aspects related to the reliability of our approach. 1. The law displayed in Eq. (1), that relates the PL intensity to the absorbed dose, was initially introduced by Soshea and coworkers to describe the creation of CCs in MgO by X-irradiation [43], and is the result of a balance between energy-mediated creation and annihilation of defects [14]. It is thanks to this elementary law that the concept itself of saturation dose Dsat could be introduced; however, it should be stressed that several phenomena were neglected in order to obtain such a simple analytical law, mainly formation of vacancies and anionic interstitials (Frenkel pairs), presence of traps that can become saturated for the combination with such interstitials, and cluster aggregations in the crystal lattice [44,45], such as colloids whose presence was allegedly detected, but only at doses higher than 106 Gy [46]. 2. Still concerning Eq. (1), the best fit of the PL z-profile shown in Fig. 2 (right) supports the conclusion that such a simple model of saturation is suitable for analyzing the PL intensity of CCs formed in LiF by 18 MeV proton beams at high doses. As a matter of fact, the dose curve plotted in Fig. 2 (right) corresponds to protons which enter the material with an energy of 18 MeV , but whose energy 103
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0.9 0.8 0.8
0.7
0.6
0.6 0.5
0.4
0.4
0.2
0.3
0 2
0.2 1
2
0
0
−1 −2
−2
0.1 0
Fig. 4. Elaboration of the PL intensity map due to F2 and F+3 CCs generated by irradiation of the LiF crystal with 18 MeV protons in the 2D-setup configuration. Left figure: PL intensity map as detected at the fluorescence microscope. Right figure: dose map obtained by elaborating the PL intensity map, as explained in the text.
gradually decreases to zero at the end of their path. Thus, information regarding an energy range from 0 to 18 MeV is stored in that dose curve. Moreover, the dose curve itself spans a dose range from 0 to about 3.67 × 105 Gy at the Bragg peak, well above the saturation dose. Being able to reproduce the PL z-profile of Fig. 2 (right) with satisfactory accuracy is a further proof that the model represented by Eq. (1) is suitable for the analysis of this kind of experimental data. 3. A common value of Dsat has been assumed for both the contributions of F2 and F+3 centers to the PL intensity. However, past experimental evidence showed that the saturation of PL intensity emitted by F2 and F+3 centers in proton-irradiated LiF takes places at different doses, even with the occurrence of quenching phenomena for the PL due to F+3 centers at high enough doses, both in LiF films [39] and crystals [40]. Hence, the resulting Dsat given in the present paper for 18 MeV protons in LiF bulk should be considered as a parameter describing an average behavior of those two kinds of CCs. This limitation is due to the fact that the two contributions to PL, one from F2 CCs and the other from F+3 CCs, cannot be separated by the spectrally-integrating detection system of the fluorescence microscope, the obtained result proves useful for a quantitative analysis especially for dose spatial distributions deposited in LiF by 18 MeV protons and analyzed with this kind of setup. 4. As already specified, the dose map elaboration in the 2D-setup suffers from relying on a thickness-averaged detection of the PL intensity I (x , y ) rather than of the actual volume distribution I (x , y, z ) . This fact causes a sort of data blurring in the derived dose map D (x , y ) , and should be kept in mind when judging the achieved results. This detrimental effect becomes more pronounced when lower proton energies are considered and/or when thicker crystals are utilized; therefore, it can be in principle mitigated with the adoption of as thin as possible samples, compatibly with the requirement of getting a high enough signal-to-noise ratio during the PL detection at the fluorescence microscope.
study (greater than 3 MeV ), however at the expense of much lower PL-intensity signal levels in the detection stage and other kinds of technical complications inherent to the deposition and utilization of thin films. Work is in progress to explore this possibility. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Research carried out within the TOP-IMPLART (Oncological Therapy with Protons—Intensity Modulated Proton Linear Accelerator for RadioTherapy) Project, funded by Lazio Region, Italy. References [1] W.B. Fowler, Physics of Color Centers, Academic Press, New York, 1968. [2] J. Nahum, D.A. Wiegand, Optical properties of some F-aggregate centers in LiF, Phys. Rev. 154 (1967) 817–830. [3] G. Baldacchini, F. Menchini, R.M. Montereali, G. Messina, A. Pace, Concentration quenching on the emission of F3+ and F2 color centers in LiF, Tech. Rep. RT/INN/ 2000/30, ENEA, 2000. [4] G. Baldacchini, F. Bonfigli, A. Faenov, F. Flora, R. Montereali, A. Pace, T. Pikuz, L. Reale, Lithium fluoride as a novel x-ray image detector for biological µ -world capture, J. Nanosci. Nanotechnol. 3 (2003) 483–486. [5] G. Baldacchini, S. Bollanti, F. Bonfigli, F. Flora, P. Di Lazzaro, A. Lai, T. Marolo, R.M. Montereali, D. Murra, A. Faenov, T. Pikuz, E. Nichelatti, G. Tomassetti, A. Reale, L. Reale, A. Ritucci, T. Limongi, L. Palladino, M. Francucci, S. Martellucci, G. Petrocelli, Soft X-ray submicron imaging detector based on point defects in LiF, Rev. Sci. Instrum. 76 (113104) (2005) 1–12. [6] A. Ustione, A. Cricenti, F. Bonfigli, F. Flora, A. Lai, T. Marolo, R.M. Montereali, G. Baldacchini, A. Faenov, T. Pikuz, L. Reale, Scanning near-field optical microscopy images of microradiographs stored in lithium fluoride films with an optical resolution of /12 , Appl. Phys. Lett. 88 (141107) (2006) 1–3. [7] S. Almaviva, F. Bonfigli, I. Franzini, A. Lai, R.M. Montereali, D. Pelliccia, A. Cedola, S. Lagomarsino, Hard X-ray contact microscopy with 250 nm spatial resolution using a LiF film detector and table-top microsource, Appl. Phys. Lett. 89 (054102) (2006) 1–3. [8] L. Reale, F. Bonfigli, A. Lai, F. Flora, A. Poma, P. Albertano, S. Bellezza, R.M. Montereali, A. Faenov, T. Pikuz, S. Almaviva, M.A. Vincenti, M. Francucci, P. Gaudio, S. Martellucci, M. Richetta, X ray microscopy of plant cells by using LiF crystal as detector, Microsc. Res. Tech. 71 (2008) 839–848. [9] D. Hampai, S.B. Dabagov, G. Della Ventura, F. Bellatreccia, M. Magi, F. Bonfigli, R.M. Montereali, High-resolution X-ray imaging by polycapillary optics and lithium fluoride detectors combination, Europhys. Lett. 96 (2011) 60010. [10] F. Bonfigli, A. Cecilia, S. Heidari Bateni, E. Nichelatti, D. Pelliccia, F. Somma, P. Vagovič, M.A. Vincenti, T. Baumbach, R.M. Montereali, In-line X-ray lensless imaging with lithium fluoride film detectors, Radiat. Meas. 56 (2013) 277–280. [11] M. Piccinini, F. Ambrosini, A. Ampollini, M. Carpanese, L. Picardi, C. Ronsivalle, F. Bonfigli, S. Libera, M.A. Vincenti, R.M. Montereali, Solid state detectors based on point defects in lithium fluoride for advanced proton beam diagnostics, J. Lumin.
6. Conclusions A method has been proposed which allows estimating the value of the saturation dose, Dsat , of proton-induced aggregate CCs in LiF crystals by iteratively comparing the results of elaborations performed to obtain dose maps and Bragg curves from the visible PL intensity distributions obtained with suitable irradiation setups. The method has been here applied to the case of 18 MeV protons. Although so far tested with crystals, the method is in principle usable also with LiF thin films, for which the data blurring effect mentioned in Section 5 almost disappears for proton energies under 104
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Evaluation of saturation dose in spatial distributions of color centers generated by 18 MeV proton beams in lithium fluoride
T
E. Nichelattia, , M. Piccininib, C. Ronsivalleb, L. Picardib, M.A. Vincentib, R.M. Monterealib ⁎
a b
ENEA C.R. Casaccia, Fusion and Technologies for Safety and Security Dept., Via Anguillarese 301, 00123 S. Maria di Galeria, Rome, Italy ENEA C.R. Frascati, Fusion and Technologies for Safety and Security Dept., Via E. Fermi 45, 00044 Frascati, Rome, Italy
ARTICLE INFO
ABSTRACT
Keywords: Radiation detectors Protons Lithium fluoride Dose map Bragg curve Color centers Photoluminescence
The paper concerns the analysis of spatial distributions of visible photoluminescence of optically active F2 and F+3 color centers created in lithium fluoride crystals by irradiation with proton beams. Spectrally integrated photoluminescent maps are detected in a fluorescence microscope and numerically elaborated to gather pieces of information regarding both the beam characteristics and the material response. A method based on two independent measurements (Bragg curve and beam transversal map) is developed to evaluate the saturation dose defined as the value above which the photoluminescence intensity begins saturating up to an asymptotic maximum. The paper describes the procedure and demonstrates its application to the experimental case of LiF crystals irradiated by a proton beam of 18 MeV nominal energy.
1. Introduction The interaction of ionizing radiation of various kinds—X-rays, γrays, UV light, accelerated ions and electrons—with the crystal lattice of lithium fluoride (LiF), either bulk or thin film, causes the formation of point defects, known as color centers (CCs), due to the release of energy in the material by the impinging radiation [1]. Some of these CCs, the F2 and F+3 defects (two electrons bound to two and three close anion vacancies, respectively) are optically active: they emit Stokesshifted photons in the visible (red and green spectral regions, respectively) when optically pumped at blue wavelengths corresponding to the M band, peaked at 450 nm, made of the two overlapping bands of F2 and F+3 CCs [2,3]. Solid-state imaging detectors for several types of ionizing radiation based on photoluminescence (PL) from CCs in LiF have been receiving in the past years more and more interest thanks to their high intrinsic spatial resolution, high dynamic range and good linearity across several orders of magnitude of the absorbed dose [4–17]. Since the CC concentration in the material is point-by-point related to the amount of absorbed energy, the intensity spatial distribution of the radiation that impinges on a LiF-based detector can be retrieved by mapping and analyzing the PL intensity by means of a properly equipped optical fluorescence microscope. The easiness of handling, excellent stability of CCs in daylight, and immediate availability for post-irradiation inspection make radiation detectors based on PL from CCs in LiF a
⁎
promising opportunity for radiation imaging purposes. Moving from the detection of CCs to their generation, it must be emphasized that accelerated hadrons are being more and more used in oncological radiotherapy [18–23]. Their penetration depth is mainly determined by their mass and energy, together with the characteristics of the material being irradiated. Differently from X-rays, accelerated hadrons release most of their energy in the final part of their path. Such a feature is very desirable in radiotherapy, because it allows to confine the deposited energy mostly within the targeted tumoral mass, while affecting the neighboring healthy tissues much less than X-rays. The depth profile of the energy that mono-energetic hadrons deposit in the material is quantitatively described by a typical curve, known as Bragg curve [24]: this curve features a slowly increasing profile with depth, followed by a sharp increase in correspondence of the so-called Bragg peak, wherein most of the deposited energy lies. Our research team has been successfully using LiF-based detectors for proton-beam diagnostics [11,13–15,25–27] within the TOP-IMPLART project for protontherapy [28]. In this project, the structure of the proton accelerator consists of a series of accelerating modules that are being gradually added to a commercial 7 MeV proton linear accelerator model PL7 by AccSys-Hitachi, which works as a low-energy injector. Measurements and tests are envisaged for each added module as part of the machine commissioning. In the present paper, our attention is more directed on the characterization of the material PL response to 18 MeV proton irradiation, in particular on a quantitative estimation of
Corresponding author. E-mail address: [email protected] (E. Nichelatti).
https://doi.org/10.1016/j.nimb.2019.12.012 Received 24 October 2019; Received in revised form 10 December 2019; Accepted 15 December 2019 0168-583X/ © 2019 Elsevier B.V. All rights reserved.
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the dose that causes saturation of the PL emitted by optically active CCs in LiF. According to a mathematical model that describes the PL intensity emitted by CCs as a function of the absorbed dose [14], a parameter called saturation dose is enough to quantify such saturation characteristics of the material. It is well known that large aggregates of F centers and macrodefects can be also created above a critical concentration and at irradiation temperatures where the diffusion of single point defects is not negligible [29,30]. Although the coloration of LiF crystals by means of ion irradiation has been the subject of intensive studies by several groups since the 70’s of the past century [29–32] (and references therein) for different ion species, ion doses and annealing conditions, and even though progress has been made on the topic both experimentally and theoretically [29,33], it is still difficult to quantitatively correlate the PL behavior with the defect concentrations as derived from optical absorption measurements [34]. One of the crucial problems concerning irradiated LiF crystals is the coexistence of several kinds of aggregate defects with often overlapping absorption bands, which makes it difficult to clearly isolate and measure the actual contributions due to the individual centers. In this regard, PL measurements are more sensitive than the absorption ones in investigating the presence of visible-emitting electronic defects and optical spectroscopy is a useful tool to separate the distinct contributions of F2 and F+3 CCs [34,35], but a fully quantitative description is still missing, especially at high irradiation doses. The purpose of the present investigation is to demonstrate how by putting together the pieces of information obtained from the analysis of specific kinds of PL intensity maps, one can estimate the saturation dose in a consistent way. The paper is organized as follows: after a description in Section 2 of the proton irradiation parameters and PL imaging setup, the theoretical method developed to evaluate the saturation dose by comparing elaborations of Bragg curves and dose maps is described in Section 3. Its application to LiF crystals irradiated by 18 MeV protons is reported in Section 4. Reliability and limits of the approach are discussed in Section 5. Finally, the obtained results are summarized in Section 6.
The nominal proton energy at the accelerator exit was 18 MeV. The beam current was 20 µA , the pulse repetition rate was 10 Hz, the charge brought by each pulse was 64 pC , and the pulse duration was 3.2 µs . The distance between the accelerator 50 μm-thick Ti exit window and the LiF crystals was 50 mm . Each irradiation consisted of a total of 2,400 pulses, which corresponds to a spatially-averaged dose absorbed at the surface of LiF (within the beam cross section) of about 1.8 × 10 4 Gy , as calculated from accelerator parameters—the uncertainty we ascribe to this value is ± 3%. The energy loss and straggling suffered by the protons for the propagation in air from the Ti window to the LiF crystals were estimated by elaborating in Matlab [36] a SRIM (version 2013.00) [37,38] simulation of 18 MeV proton propagation in air (89,999 protons, quick calculation algorithm). The resulting values were: mean energy loss of 150 keV and standard deviation of the energy distribution (straggling) of 21 keV . After the irradiations, the visible spectrally integrated PL images emitted by the spatial distributions of F2 and F+3 CCs generated in LiF due to the proton beam interaction with the lattice were acquired at 2× magnification in a Nikon Eclipse 80-i fluorescence microscope equipped with a Hg lamp and an Andor Neo s-CMOS camera [26]. To perform Bragg curve analysis as in [15], a PL-intensity depth profile was extracted from the digital image acquired after the 1D-setup irradiation by averaging along the x-direction the intensities of the pixels contained in rectangle R2 of Fig. 1. All the numerical elaborations appearing in this paper were performed in Matlab with specifically written codes. 3. Theory Under the simplifying hypothesis that the intensity of PL emitted by CCs in LiF is point-by-point proportional to their concentration, the relationship existing between the PL intensity I and the absorbed dose D is assumed to be ruled by the formula [14]
I (D ) = I
2. Materials and methods
1
exp
D Dsat
,
(1)
where I is the asymptotic maximum value that the PL intensity would assume for infinitely large dose, and Dsat , the saturation dose, is a parameter representing the dose above which the saturation of I becomes evident. The above formula represents an approximately linear growth of I with D, followed by saturation for high values of D. For the concentrations of complex centers in LiF, like the F2 and F+3 defects, other investigations—regarding generation of CCs in LiF by ion irradiation—report more elaborated models that account for the aggregation mechanisms of F centers [31,33]. It is not clear yet how to quantitatively correlate the PL intensity behavior with the defect concentrations as derived from optical absorption measurements, on which those studies rely. Best fits of available experimental data, such as those reported in [25,39–41] for 3 and 7 MeV protons, show that Eq. (1) is suitable to describe the behavior of spectrally integrated PL vs. dose (or absorbed energy) from CCs generated by low-energy protons in LiF. On the other hand, our attempts to best fit the same data with more elaborated models led to less satisfying results. We assume the same conclusion in favor of Eq. (1) to hold also for the present case of 18 MeV protons. The comparison of the PL-intensity spatial distributions obtained in the 2D-setup and 1D-setup (Fig. 1) allows finding a common value of the saturation dose Dsat , as explained in the following.
The samples were two polished 10 × 10 × 1 mm3 LiF crystals, commercially available by Macrooptica Ltd. They were irradiated at normal incidence—one on its 10 × 10 mm2 face (‘2D-setup’), the other on its 10 × 1 mm2 side face (‘1D-setup’), see Fig. 1—in air at room temperature with an accelerated proton beam generated by the linear accelerator that is being developed at ENEA Frascati for the TOP-IMPLART project [28]. The irradiation parameters were the same for both setups.
Fig. 1. Scheme of the setups for the proton irradiations of LiF crystals. Left side: 2D-setup for dose mapping reconstruction. Right side: 1D-setup for Bragg curve analysis. In the 1D-setup, rectangle R2 indicates the area considered to extract the PL-intensity depth profile from the PL image detected at the fluorescence microscope, while rectangle R1 is the corresponding area on the thin side of the crystal within which the entrance dose Din is evaluated (see Section 3.2). The same rectangle R1 is shown also in the 2D-setup, where it is centered around the peak of the PL-intensity distribution; the mean dose at the surface within R1 in the 2D-setup is assumed to be equal to that within R1 in the 1D-setup, see Section 3.3.
3.1. 2D dose map Indicating with (x , y ) the spatial coordinates of the plane coinciding with the proton-irradiated 10 × 10 mm2 face of the LiF crystal in the 2Dsetup—see Fig. 1—the map of absorbed dose, D (x , y ) , is obtained by 101
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properly elaborating the distribution of PL intensity I (x , y ) that is emitted by the optically-active CCs in the material [14,26]. If the proton beam fluence were low enough, one could consider I to be approximately proportional to D in every point of the distribution, but for higher fluences, as those considered in the present paper, saturation phenomena have to be taken into account by using Eq. (1). Therefore, the dose map is calculated from the PL intensity distribution by inverting Eq. (1),
D x, y =
Dsat ln 1
I (x , y ) . I
at the value found by the best fit, Dsat must become larger (smaller) if Din is increased (decreased). To apply the procedure of [15], LET curves LE, E (z ) were simulated in SRIM at several energies E and energy spreads E —the values of these parameters were tentatively chosen to span ranges that included the sought actual values and to be dense enough for calculating LET curves at intermediate (E , E ) points by linear interpolation. These LE, E (z ) were later processed by means of Matlab, according to what follows. After calculating the related dose-depth profiles DE, E (z ) = LE, E (z )/ —where is the proton beam fluence at the material entrance point and is the material density—corresponding PL-intensity profiles IE, E (z ) were obtained from Eq. (1) for a set value of the fit parameter R Din / Dsat , from which the argument of the exponential function is calculated [15]. These IE, E (z ) profiles were regarded to as elements of a lookup table, so that test PL-intensity profiles with desired intermediate energies and energy spreads could be calculated by linear interpolation; eventually, a least-square optimization allowed finding the best fitting PL-intensity by varying three fit parameters: energy, energy spread, and R [15].
(2)
In order to successfully perform such an inversion, the values of Dsat and I need to be known. Regarding Dsat , it is going to be treated as an adjustable input parameter, as later discussed in Section 4. The intensity I (x , y ) that is detected at the microscope is due to CCs found at various depths in the LiF crystal. This fact means that the detected I (x , y ) can be considered to be the z-average of a more general I (x , y, z ) volume distribution. Assuming the mean absorbed dose D over the irradiated volume V to be experimentally known, one can integrate Eq. (2), obtaining
D =
Dsat S
S
ln 1
I (x , y ) dx dy , I
3.3. Saturation dose estimation
(3)
In the previous Sections 3.1 and 3.2, the saturation dose Dsat was linked to two other quantities: Dmax for the analysis of dose maps in the 2D-setup, and Din for the analysis of Bragg curves in the 1D-setup. It has been pointed out how the variations of the Dsat value are driven by those of Dmax and Din with opposite behaviors: while Dsat increases (decreases) together with Din , it decreases (increases) for increasing (decreasing) Dmax . Because Dsat should be a characteristic parameter of the material, suitable values of Dmax and Din should in principle exist to which a physically consistent value of Dsat corresponds. The above conclusion suggests an experimental approach to evaluate Dsat . If the irradiations in the 2D-setup and 1D-setup are made under the same experimental conditions (proton energy, fluence, etc.), and if the geometry of the 1D-setup is such that rectangle R1 coincides with the most intense part of the proton beam (see Fig. 1), then Din should be equal to Dmax —or approximately equal, if one considers (a) that rectangle R1 is likely to include also doses that are slightly lower than Dmax , and (b) that D (x , y ) is a z-average of the actual volume distribution of dose. Therefore, if Din and Dmax are both increased or decreased, Dsat will change in opposite directions depending on which type of analysis is being performed, either dose map calculation or Bragg curve best fit. As a consequence, defining Dsat,2D {Dsat ; from dose map} and Dsat,1D {Dsat ; from Bragg curve} , smaller values of Dsat,1D should correspond to larger values of Dsat,2D , and vice versa. Hence, a common value of Dsat,2D and Dsat,1D should exist that is compatible with both dose map analysis and Bragg best fit; this value is assumed to be the most plausible one for Dsat .
where the irradiated volume V is formed by a suitable area S in the plane Oxy with thickness h = 1 mm along z. In the surface integral, the further simplifying assumption that the integrand function approximates the z-average of ln[1 I (x , y, z )/ I ] is made. (It should be noticed that, for the proton energy considered in this paper, 18 MeV, the Bragg peak is found in LiF at a depth of 1.6 mm , that is well beyond the thickness of the LiF crystal.) By numerically solving Eq. (3), the value of the unknown I can be determined and used in Eq. (2) to finally obtain D (x , y ) . For what above said, also D (x , y ) has to be understood as an approximate z-average of the actual volume distribution of dose. Due to the shape of the function ln(1 t ) , that monotonically grows with t (0 t < 1), the solution I of Eq. (3) generally depends on Dsat in the following way: for a certain D , to larger (smaller) values of Dsat , larger (smaller) values of I correspond to obtain a smaller (larger) I (x , y )/ I ] dx dy . Since also the t-derivative of ln(1 t ) S ln[1 monotonically grows with t, the largest-valued parts of ln[1 I (x , y )/ I ] change more than its surface-average, thus are more affected than the latter by changes in Dsat . It can be concluded that, according to Eq. (2), the largest-valued portions of D (x , y ) —in particular, its maximum Dmax —should become smaller if Dsat becomes larger, and vice versa, for the right member of Eq. (3) to keep being equal to the given D . 3.2. 1D Bragg curve
4. Results
An experimental evaluation of the Bragg curve of protons in LiF can be obtained by elaborating a thin slice—rectangle R2 in Fig. 1—of the PL image that is detected on the 10 × 10 mm2 face of the crystal after irradiation in the 1D-setup. Such an approach practically corresponds to analyzing a mono-dimensional I (z ) PL-intensity profile, where z is the depth coordinate, with z = 0 at the air-LiF interface and z > 0 inside the material. The I (z ) profile is obtained by averaging over x the intensities of the pixels found within rectangle R2. This kind of analysis was the subject of recent publications by our research team, both in presence [15] and in absence [27,42] of CC saturation. In the former case, we demonstrated for 7 MeV protons how a suitable best fit leads to the full recovery of the proton Bragg curve in LiF, and that the ratio R Din / Dsat of the entrance dose Din —that is, the dose absorbed by LiF within rectangle R1 (Fig. 1, right side)—to the saturation dose Dsat can be evaluated from the best fit, so that Dsat can be estimated from R provided Din is known [15]. To keep R unchanged
For irradiation of LiF bulk with 18 MeV protons, a SRIM simulation (99,999 protons, quick calculation algorithm) showed a nearly linear increase of the linear energy transfer (LET) across the crystal 1 mm thickness: approximately from 6 eV/nm to 9 eV/nm . Therefore, an average LET of about 7.5 eV/nm is expected within the crystal in the 2Dsetup, a value that is 25% larger than the LET at the crystal surface. Consistently, by using the known average dose 1.8 × 10 4 Gy absorbed at the LiF crystal surface in the 2D-setup, a 25% higher average absorbed dose within the crystal volume, D = 2.25 × 10 4 Gy , is expected. Taking into account this value for the calculation of I by means of Eq. (3)—recalling that the I (x , y ) therein appearing represents an average along z of the PL contributions from various depths in the crystal—the procedure to find a reliable value of Dsat from our elaborations was the following. 102
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Table 1 Values of the 2D and 1D elaborations as obtained by varying Dsat,2D .
Fig. 2. Elaboration of the PL intensity depth profile of a LiF crystal irradiated with 18 MeV protons in the 1D-setup. Left figure: PL intensity map detected at the fluorescence microscope due to F2 and F+3 CCs generated by the irradiation; rectangle R2 (see Fig. 1)—whose x-width corresponds to 30 pixels of 3.26 μm size—frames the area from which the PL intensity profile along z was obtained by averaging the pixel intensities in the x direction. Right figure: obtained PL intensity depth profile (dots) and its best fit (solid line), for which the approach explained in [15] was applied; the dose z-profile, calculated from the SRIM simulated LET curve, is also shown (dashed line).
1. The ratio R = Din / Dsat is found from the best fit of the Bragg curve, as explained in [15]. 2. A test value of Dsat,2D is chosen. The unknown I is calculated by numerically solving Eq. (3). The obtained I , together with Dsat,2D, is inserted into Eq. (2) to retrieve the dose map D (x , y ) . The average Dmax of the most intense part of D (x , y ) , coincident with the small rectangle R1 (Fig. 1, left side) is then calculated, its value being close to Dmax and more accurate to apply the approach explained in Section 3.3. 3. Because of the assumption of a 25% higher average dose within the crystal than at its surface, Din is set equal to the value of Dmax diminished by 25%; Din is then used to evaluate Dsat,1D from the known ratio R, by applying Dsat,1D = Din /R . 4. The so obtained Dsat,1D is compared with the test Dsat,2D.
Dsat,2D (105 Gy)
Dmax (10 4 Gy)
Din (10 4 Gy)
Dsat,1D (105 Gy)
1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35
9.246 9.146 9.059 8.981 8.912 8.850 8.794 8.743
7.397 7.317 7.247 7.185 7.130 7.080 7.035 6.995
1.209 1.196 1.184 1.174 1.165 1.157 1.150 1.143
1.17
8.953 ± 0.095
± ± ± ± ± ± ± ±
0.106 0.102 0.099 0.096 0.093 0.091 0.089 0.087
± ± ± ± ± ± ± ±
0.085 0.082 0.079 0.077 0.075 0.073 0.071 0.070
7.162 ± 0.076
± ± ± ± ± ± ± ±
0.021 0.021 0.020 0.020 0.019 0.019 0.019 0.018
1.171 ± 0.020
Fig. 3. Dependence of the saturation dose estimated from the Bragg curve analysis, Dsat,1D , on the same quantity estimated from the dose map analysis, Dsat,2D . The intersection with the quadrant bisector (dashed line), in which Dsat,1D = Dsat,2D , is represented by an empty circle. The confidence bars correspond to 95% probability.
Dsat = (1.171 ± 0.020) × 105 Gy . Using this value, a definitive dose map could be obtained from the PL intensity map detected at the fluorescence microscope; both of these maps are shown in Fig. 4.
The above procedure has to be iterated from step 2 to step 4 by properly changing Dsat,2D , until matching values of Dsat,1D and Dsat,2D are obtained. Regarding step 1, the depth profile of the PL intensity was best fitted by applying the approach explained in [15]. Fig. 2 shows the PL intensity map from which the depth profile—also shown together with its best fitting curve—was extracted as an x-average of the pixelintensity values inside rectangle R2. The value of the ratio of input dose to saturation dose for the Bragg curve analysis resulted to be R = 0.6119 ± 0.0037 . Other meaningful parameters were provided by the best fit, as in [15]: mean proton energy, E = (18.24 ± 0.05) MeV ; standard deviation of the proton energy distribution, E = (143 ± 5) keV ; ratio of the dose DBP at the Bragg peak to the saturation dose, DBP /Dsat = 3.13 ± 0.30 . At step 2, the initial value chosen for Dsat,2D was 1.00 × 105 Gy . Because the Dsat,1D resulting from step 3 was higher than this value, Dsat,2D was incrementally increased, obtaining in this way several values of Dsat,1D that are listed in Table 1 and plotted in Fig. 3. In Table 1, the third column was calculated by decreasing by 25% the second column values to estimate the surface dose Din for Bragg curve analysis. It can be noticed how Dsat,1D and Dsat,2D move in opposite directions, as expected by our reasoning in Section 3.3; the intersection point between 1.15 × 105 Gy and 1.20 × 105 Gy was eventually found and the result is reported in the bottom row of Table 1. The same intersection point is drawn in Fig. 3 as an empty circle, together with a confidence bar which represents the uncertainty in the determination of its value with 95% probability. According to the results of this comparative analysis, it can be concluded that the most reliable value for the saturation dose in LiF (18.24 ± 0.05) MeV bulk irradiated with protons is
5. Discussion Although the procedure to evaluate the Dsat for CCs in LiF crystals worked as expected when applied to the considered experimental case of 18 MeV protons, it is worth clarifying some aspects related to the reliability of our approach. 1. The law displayed in Eq. (1), that relates the PL intensity to the absorbed dose, was initially introduced by Soshea and coworkers to describe the creation of CCs in MgO by X-irradiation [43], and is the result of a balance between energy-mediated creation and annihilation of defects [14]. It is thanks to this elementary law that the concept itself of saturation dose Dsat could be introduced; however, it should be stressed that several phenomena were neglected in order to obtain such a simple analytical law, mainly formation of vacancies and anionic interstitials (Frenkel pairs), presence of traps that can become saturated for the combination with such interstitials, and cluster aggregations in the crystal lattice [44,45], such as colloids whose presence was allegedly detected, but only at doses higher than 106 Gy [46]. 2. Still concerning Eq. (1), the best fit of the PL z-profile shown in Fig. 2 (right) supports the conclusion that such a simple model of saturation is suitable for analyzing the PL intensity of CCs formed in LiF by 18 MeV proton beams at high doses. As a matter of fact, the dose curve plotted in Fig. 2 (right) corresponds to protons which enter the material with an energy of 18 MeV , but whose energy 103
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0.9 0.8 0.8
0.7
0.6
0.6 0.5
0.4
0.4
0.2
0.3
0 2
0.2 1
2
0
0
−1 −2
−2
0.1 0
Fig. 4. Elaboration of the PL intensity map due to F2 and F+3 CCs generated by irradiation of the LiF crystal with 18 MeV protons in the 2D-setup configuration. Left figure: PL intensity map as detected at the fluorescence microscope. Right figure: dose map obtained by elaborating the PL intensity map, as explained in the text.
gradually decreases to zero at the end of their path. Thus, information regarding an energy range from 0 to 18 MeV is stored in that dose curve. Moreover, the dose curve itself spans a dose range from 0 to about 3.67 × 105 Gy at the Bragg peak, well above the saturation dose. Being able to reproduce the PL z-profile of Fig. 2 (right) with satisfactory accuracy is a further proof that the model represented by Eq. (1) is suitable for the analysis of this kind of experimental data. 3. A common value of Dsat has been assumed for both the contributions of F2 and F+3 centers to the PL intensity. However, past experimental evidence showed that the saturation of PL intensity emitted by F2 and F+3 centers in proton-irradiated LiF takes places at different doses, even with the occurrence of quenching phenomena for the PL due to F+3 centers at high enough doses, both in LiF films [39] and crystals [40]. Hence, the resulting Dsat given in the present paper for 18 MeV protons in LiF bulk should be considered as a parameter describing an average behavior of those two kinds of CCs. This limitation is due to the fact that the two contributions to PL, one from F2 CCs and the other from F+3 CCs, cannot be separated by the spectrally-integrating detection system of the fluorescence microscope, the obtained result proves useful for a quantitative analysis especially for dose spatial distributions deposited in LiF by 18 MeV protons and analyzed with this kind of setup. 4. As already specified, the dose map elaboration in the 2D-setup suffers from relying on a thickness-averaged detection of the PL intensity I (x , y ) rather than of the actual volume distribution I (x , y, z ) . This fact causes a sort of data blurring in the derived dose map D (x , y ) , and should be kept in mind when judging the achieved results. This detrimental effect becomes more pronounced when lower proton energies are considered and/or when thicker crystals are utilized; therefore, it can be in principle mitigated with the adoption of as thin as possible samples, compatibly with the requirement of getting a high enough signal-to-noise ratio during the PL detection at the fluorescence microscope.
study (greater than 3 MeV ), however at the expense of much lower PL-intensity signal levels in the detection stage and other kinds of technical complications inherent to the deposition and utilization of thin films. Work is in progress to explore this possibility. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgements Research carried out within the TOP-IMPLART (Oncological Therapy with Protons—Intensity Modulated Proton Linear Accelerator for RadioTherapy) Project, funded by Lazio Region, Italy. References [1] W.B. Fowler, Physics of Color Centers, Academic Press, New York, 1968. [2] J. Nahum, D.A. Wiegand, Optical properties of some F-aggregate centers in LiF, Phys. Rev. 154 (1967) 817–830. [3] G. Baldacchini, F. Menchini, R.M. Montereali, G. Messina, A. Pace, Concentration quenching on the emission of F3+ and F2 color centers in LiF, Tech. Rep. RT/INN/ 2000/30, ENEA, 2000. [4] G. Baldacchini, F. Bonfigli, A. Faenov, F. Flora, R. Montereali, A. Pace, T. Pikuz, L. Reale, Lithium fluoride as a novel x-ray image detector for biological µ -world capture, J. Nanosci. Nanotechnol. 3 (2003) 483–486. [5] G. Baldacchini, S. Bollanti, F. Bonfigli, F. Flora, P. Di Lazzaro, A. Lai, T. Marolo, R.M. Montereali, D. Murra, A. Faenov, T. Pikuz, E. Nichelatti, G. Tomassetti, A. Reale, L. Reale, A. Ritucci, T. Limongi, L. Palladino, M. Francucci, S. Martellucci, G. Petrocelli, Soft X-ray submicron imaging detector based on point defects in LiF, Rev. Sci. Instrum. 76 (113104) (2005) 1–12. [6] A. Ustione, A. Cricenti, F. Bonfigli, F. Flora, A. Lai, T. Marolo, R.M. Montereali, G. Baldacchini, A. Faenov, T. Pikuz, L. Reale, Scanning near-field optical microscopy images of microradiographs stored in lithium fluoride films with an optical resolution of /12 , Appl. Phys. Lett. 88 (141107) (2006) 1–3. [7] S. Almaviva, F. Bonfigli, I. Franzini, A. Lai, R.M. Montereali, D. Pelliccia, A. Cedola, S. Lagomarsino, Hard X-ray contact microscopy with 250 nm spatial resolution using a LiF film detector and table-top microsource, Appl. Phys. Lett. 89 (054102) (2006) 1–3. [8] L. Reale, F. Bonfigli, A. Lai, F. Flora, A. Poma, P. Albertano, S. Bellezza, R.M. Montereali, A. Faenov, T. Pikuz, S. Almaviva, M.A. Vincenti, M. Francucci, P. Gaudio, S. Martellucci, M. Richetta, X ray microscopy of plant cells by using LiF crystal as detector, Microsc. Res. Tech. 71 (2008) 839–848. [9] D. Hampai, S.B. Dabagov, G. Della Ventura, F. Bellatreccia, M. Magi, F. Bonfigli, R.M. Montereali, High-resolution X-ray imaging by polycapillary optics and lithium fluoride detectors combination, Europhys. Lett. 96 (2011) 60010. [10] F. Bonfigli, A. Cecilia, S. Heidari Bateni, E. Nichelatti, D. Pelliccia, F. Somma, P. Vagovič, M.A. Vincenti, T. Baumbach, R.M. Montereali, In-line X-ray lensless imaging with lithium fluoride film detectors, Radiat. Meas. 56 (2013) 277–280. [11] M. Piccinini, F. Ambrosini, A. Ampollini, M. Carpanese, L. Picardi, C. Ronsivalle, F. Bonfigli, S. Libera, M.A. Vincenti, R.M. Montereali, Solid state detectors based on point defects in lithium fluoride for advanced proton beam diagnostics, J. Lumin.
6. Conclusions A method has been proposed which allows estimating the value of the saturation dose, Dsat , of proton-induced aggregate CCs in LiF crystals by iteratively comparing the results of elaborations performed to obtain dose maps and Bragg curves from the visible PL intensity distributions obtained with suitable irradiation setups. The method has been here applied to the case of 18 MeV protons. Although so far tested with crystals, the method is in principle usable also with LiF thin films, for which the data blurring effect mentioned in Section 5 almost disappears for proton energies under 104
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