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Studies of experimentally determined etch-rate ratios in CR-39 for ions of different kinds and energies
Radiation Measurements 35 (2002) 183 – 187
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Studies of experimentally determined etch-rate ratios in CR-39 for ions of di'erent kinds and energies B. D,orschel ∗ ,D. Hermsdorf, K. Kadner Physics Department, Institute of Radiation Protection Physics, Dresden University of Technology, D-01062 Dresden, Germany Received 16 October 2001; received in revised form 22 January 2002; accepted 1 February 2002
Abstract The ratio of track etch rate to bulk etch rate is correlated with the energy transfer of a penetrating ion. For quantifying this correlation the etch-rate ratio, V , in dependence on the restricted energy loss, REL, for ions of di'erent kinds and energies was studied. The track etch rate was taken as depth-dependent function derived from track length measurements. A unique V (REL) relationship was found for all cases where the reduction of the track etch rate at the beginning of the etching process is of little in;uence. Etch-rate ratios determined after the common method of track diameter evaluation have been found to c 2002 Elsevier Science Ltd. All rights be systematically too low with the exception of the region near the detector surface. reserved. Keywords: Etch-rate ratio; Track length; Track diameter; Track etch rate; Restricted energy loss; CR-39
1. Introduction The ratio of the track etch rate, vT , to the bulk etch rate, vB , is of fundamental interest for understanding the track formation process in solid-state nuclear track detectors. Many attempts have been made to
Presented at the 20th International Conference on Nuclear Tracks in solids, Portoroz, 2000. ∗ Corresponding author. Tel.: +49-351-463-32566; fax: +49351-463-37040. E-mail address: [email protected] (B. D,orschel).
The etch-rate ratio was studied by many authors using the track diameters measured at the detector surface at a given etching time. The derivation of V was made in these cases either presuming a time-independent track etch rate vT (Somogyi, 1980; Baiocchi et al., 1995) or using a function for vT with several free parameters which have to be
c 2002 Elsevier Science Ltd. All rights reserved. 1350-4487/02/$ - see front matter PII: S 1 3 5 0 - 4 4 8 7 ( 0 2 ) 0 0 0 4 9 - 5
184
B. D'orschel et al. / Radiation Measurements 35 (2002) 183 – 187
2. Fundamentals Quantities tested for correlation with the track etch rate were the total energy loss per unit path, dE=d x, and the quantity z 2 =2 where z means the charge number of the ion and = v=c is the ratio of the particle velocity to the velocity of light. The results matched with the vT data within certain limits but did not yield a generalised relationship. More promising seems to be the use of the restricted energy loss, REL, where contribution to the track formation is assumed only by the energy transfer of low-energy delta electrons with energies ! up to a threshold energy !0 . The !0 values found in the literature vary between 200 and 1000 eV (Benton and Nix, 1969; Doke et al., 1995; Yadav, 1995). Frequently, the correlation of REL350 (i.e. !0 =350 eV) with the etch-rate ratio has been studied. The data basis for REL350 can be established by ion transport and data processing programs, for instance by the StopPow program (D,orschel and Henniger, 2000). In the simplest way, the track etch rate, vT , is determined from the track diameters, d, measured after the etching time, t, on the detector surface using the relationship v T = vB
4vB2 t 2 + d2 : 4vB2 t 2 − d2
(1)
This formula is valid only when the etch pit can be described by a cone which means that the track etch rate vT has to be time-independent. However, because the track etch rate is correlated with the energy loss of the charged particles, a distinct variation of vT along the trajectory has to be expected. The variable track etch rate has been studied in the former work for CR-39 of TASTRAK type (Track Analysis Systems Ltd., UK) perpendicularly irradiated with protons, deuterons, alpha particles and lithium ions (D,orschel et al., 1997, 1999). The vT data for a given initial ion energy, W , were obtained by the derivation of the functions for the time-dependent track lengths, L, measured by the method described by D,orschel et al. (1997). The results for the track etch rate vT (W; x) as a function of the depth x within the detector follow from vT (W; t) =
dL (W; t) + vB dt
(2)
substituting the variable t by the depth x according to x = L + vB t:
(3)
The bulk etch rate was vB = 1:83 m=h for the detector batch used for proton and alpha particle irradiation, whereas the detectors irradiated by deuterons and lithium ions are characterised by vB = 1:73 m=h. Since the normalised ratio V = vT =vB is used for the further evaluation, these small di'erences in vB do not play any role. The track etch rate vT (W; x) was determined for ions of di'erent kinds and initial
energy W . On the other hand, the restricted energy loss, REL350 (W; x), was computed as a function of W and x using the program StopPow (D,orschel and Henniger, 2000). By attaching vT (W; x) to REL350 (W; x) at the same values for W and x the function V = f (REL350 ) follows. The results are expected to agree approximately with the values resulting from the simple formula (1) if the track etch rate varies only slowly. This is the case for low-energy light ions only at the beginning of the etching process at a small depth below the detector surface. 3. Results Fig. 1 shows the etch-rate ratio determined as a function of REL350 for protons, alpha particles and lithium ions with a wide variety of the initial particle energy. Since the results for several energies are congruent, their discrimination by di'erent symbols is not recognisable in Fig. 1 in these cases. The data for deuterons were not added to the presentation for the purpose of clarity. They match the results for protons quite well as demonstrated in Fig. 2. The functions found for the etch-rate ratio along proton, deuteron and alpha-particle-induced tracks do not show any systematic dependence on the initial particle energy. The standard deviation (1) for V taking into account the whole data set at the corresponding REL350 value did not exceed 12%. This seems to be smaller than that expected from the visual impression on the width of variation in Figs. 1 and 2. However, as mentioned above, several points at a given REL350 value were congruent and their discrimination by di'erent symbols is not recognisable from the
B. D'orschel et al. / Radiation Measurements 35 (2002) 183 – 187
185
Fig. 1. Etch-rate ratio, V , as a function of restricted energy loss, REL350 , for protons, alpha particles and lithium ions of di'erent initial energies.
Fig. 2. Etch-rate ratio, V , as a function of restricted energy loss, REL350 , for protons and deuterons of di'erent initial energies. The line corresponds to the generalised curve from Fig. 1.
not be tested experimentally because the tracks were too short for the length measurement in these cases. Results for V (REL) were also presented by other authors who extracted the track etch rate from the track diameters after Eq. (1). A comparison of these results with the data given in Fig. 1 showed that the curves presented in the literature are more ;at (see e.g. Baiocchi et al., 1995). The reason for this e'ect is that vT following from Eq. (1) is depth-independent, whereas the vT values resulting from Eq. (2) increase with the depth and, therefore, with REL. An agreement of the results should, however, be expected for
REL350 at the detector surface. This corresponds to REL350 for the initial ion energy. Fig. 3 shows the results in comparison with the data published by other authors (Baiocchi et al., 1995) for protons and alpha particles as well as beryllium and silicon ions. The agreement is satisfying taking into account the experimental uncertainties. Furthermore, the results for lithium ions determined after Eqs. (1) and (2), respectively, were compared by con
186
B. D'orschel et al. / Radiation Measurements 35 (2002) 183 – 187
Fig. 3. Etch-rate ratio at the detector surface, V0 , as a function of the restricted energy loss, REL350 . The line corresponds to the results for protons, alpha particles and lithium ions with initial energies given in Fig. 1. The points represent data of Baiocchi et al. for ions with initial energies given at the corresponding site.
Fig. 4. Etch-rate ratio, V , as a function of restricted energy loss, REL350 , for lithium ions of di'erent initial energies. The REL350 values correspond to the region beyond the Bragg peak. The line characterises the results from Fig. 1 for REL350 values below the Bragg peak.
trajectory should, however, be extracted from the depthdependent track etch rate after Eqs. (2) and (3). In Figs. 1–3, the V (REL350 ) relationship is given for ions slowed-down up to the Bragg peak. The experimental determination of the depth-dependent track etch rate also allows, however, to extract etch-rate ratios for REL350 values beyond the Bragg peak. For this purpose vT (W; x) data are used for x values between the position of the maximum and that depth where vT drops to vB . Fig. 4 shows the results for lithium ions of di'erent initial energies. The curves coin-
cide with each other where the standard deviation at a given REL350 value does not exceed 16%. Besides, a good agreement with the generalised curve for V (REL350 ) derived from the results in Fig. 1 for REL350 values on the other side of the Bragg peak (using the 10:96 MeV 7 Li data) is observed. 4. Discussion and conclusions The etch-rate ratio found for protons, deuterons, alpha particles and 7 Li ions of di'erent energies can be correlated
B. D'orschel et al. / Radiation Measurements 35 (2002) 183 – 187
to the restricted energy loss resulting in a unique function V (REL350 ) within certain limits. The deviations observed for low-energy lithium ions at REL350 values corresponding to small depths within the detector seem to result from a reduced track etching at the beginning of the etching process. That means, the track etch rate is lower than expected. This e'ect is marked more distinctly for low ion energies where very-high track etch rates are obtained, whereas for higher ion energies the track etch reduction seems to play no role. Also, at greater depths within the detector this e'ect is not pronounced for the ions considered as demonstrated by the agreement in V (REL350 ) for REL350 values beyond the Bragg peak. A possible explanation could be that at high REL350 values near the detector surface, the track etch rate does not jump to the expected high values but a continuous increase occurs. This behaviour is more distinct the heavier the ion is. In the case of protons, deuterons and alpha particles it was not observed at the particle energies considered here but it cannot be excluded that it occurs likewise at lower energies. The main conclusion from these studies is, that a generalised V (REL350 ) relationship can be given for all the cases where the reduction of the track etch rate at the beginning of the etching process is only of little in;uence. Otherwise, the V (REL350 ) relationship has to be speci
187
Benton, E.V., Nix, W.D., 1969. The restricted energy loss criterion for registration of charged particles in plastics. Nucl. Instrum. Methods 67, 343–352. Doke, T., Hayashi, T., Nagaoka, S., Ogura, K., Takeuchi, R., 1995. Estimation of dose equivalent in STS-47 by a combination of TLDs and CR-39. Radiat. Meas. 24, 75–82. D,orschel, B., Bretschneider, R., Hermsdorf, D., Kadner, K., K,uhne, H., 1999. Measurement of the track etch rates along proton and alpha particle trajectories in CR-39 and calculation of the detection eBciency. Radiat. Meas. 31, 103–108. D,orschel, B., F,ulle, D., Hartmann, H., Hermsdorf, D., Kadner, K., Radlach, Ch., 1997. Measurement of track parameters and etch rates in proton-irradiated CR-39 detectors and simulation of neutron dosemeter responses. Radiat. Prot. Dosim. 69, 267–274. D,orschel, B., Henniger, J., 2000. The program StopPow—a useful tool for computation of energy loss and range of light ions in SSNTD’s. Nucl. Instrum. Methods (B) 171, 423–430. Fromm, M., Membrey, F., El Rahamany, Chambaudet, A., 1993. Principle of light ions micromapping and dosimetry using CR-39 polymeric detector: modelized and experimental uncertainties. Nucl. Tracks Radiat. Meas. 21, 357–365. G,unther, W., Leugner, D., Becker, E., Flesch, F., Heinrich, W., H,untrup, G., Reitz, G., R,ocher, H., Streibel, T., 1999. Energy spectrum of iron nuclei measured inside the MIR space craft using CR-39 track detectors. Radiat. Meas. 31, 585–590. Somogyi, G., 1980. Development of etched nuclear tracks. Nucl. Instrum. Methods 173, 21–42. Yadav, J.S., 1995. Charged particle identi
www.elsevier.com/locate/radmeas
Studies of experimentally determined etch-rate ratios in CR-39 for ions of di'erent kinds and energies B. D,orschel ∗ ,D. Hermsdorf, K. Kadner Physics Department, Institute of Radiation Protection Physics, Dresden University of Technology, D-01062 Dresden, Germany Received 16 October 2001; received in revised form 22 January 2002; accepted 1 February 2002
Abstract The ratio of track etch rate to bulk etch rate is correlated with the energy transfer of a penetrating ion. For quantifying this correlation the etch-rate ratio, V , in dependence on the restricted energy loss, REL, for ions of di'erent kinds and energies was studied. The track etch rate was taken as depth-dependent function derived from track length measurements. A unique V (REL) relationship was found for all cases where the reduction of the track etch rate at the beginning of the etching process is of little in;uence. Etch-rate ratios determined after the common method of track diameter evaluation have been found to c 2002 Elsevier Science Ltd. All rights be systematically too low with the exception of the region near the detector surface. reserved. Keywords: Etch-rate ratio; Track length; Track diameter; Track etch rate; Restricted energy loss; CR-39
1. Introduction The ratio of the track etch rate, vT , to the bulk etch rate, vB , is of fundamental interest for understanding the track formation process in solid-state nuclear track detectors. Many attempts have been made to
Presented at the 20th International Conference on Nuclear Tracks in solids, Portoroz, 2000. ∗ Corresponding author. Tel.: +49-351-463-32566; fax: +49351-463-37040. E-mail address: [email protected] (B. D,orschel).
The etch-rate ratio was studied by many authors using the track diameters measured at the detector surface at a given etching time. The derivation of V was made in these cases either presuming a time-independent track etch rate vT (Somogyi, 1980; Baiocchi et al., 1995) or using a function for vT with several free parameters which have to be
c 2002 Elsevier Science Ltd. All rights reserved. 1350-4487/02/$ - see front matter PII: S 1 3 5 0 - 4 4 8 7 ( 0 2 ) 0 0 0 4 9 - 5
184
B. D'orschel et al. / Radiation Measurements 35 (2002) 183 – 187
2. Fundamentals Quantities tested for correlation with the track etch rate were the total energy loss per unit path, dE=d x, and the quantity z 2 =2 where z means the charge number of the ion and = v=c is the ratio of the particle velocity to the velocity of light. The results matched with the vT data within certain limits but did not yield a generalised relationship. More promising seems to be the use of the restricted energy loss, REL, where contribution to the track formation is assumed only by the energy transfer of low-energy delta electrons with energies ! up to a threshold energy !0 . The !0 values found in the literature vary between 200 and 1000 eV (Benton and Nix, 1969; Doke et al., 1995; Yadav, 1995). Frequently, the correlation of REL350 (i.e. !0 =350 eV) with the etch-rate ratio has been studied. The data basis for REL350 can be established by ion transport and data processing programs, for instance by the StopPow program (D,orschel and Henniger, 2000). In the simplest way, the track etch rate, vT , is determined from the track diameters, d, measured after the etching time, t, on the detector surface using the relationship v T = vB
4vB2 t 2 + d2 : 4vB2 t 2 − d2
(1)
This formula is valid only when the etch pit can be described by a cone which means that the track etch rate vT has to be time-independent. However, because the track etch rate is correlated with the energy loss of the charged particles, a distinct variation of vT along the trajectory has to be expected. The variable track etch rate has been studied in the former work for CR-39 of TASTRAK type (Track Analysis Systems Ltd., UK) perpendicularly irradiated with protons, deuterons, alpha particles and lithium ions (D,orschel et al., 1997, 1999). The vT data for a given initial ion energy, W , were obtained by the derivation of the functions for the time-dependent track lengths, L, measured by the method described by D,orschel et al. (1997). The results for the track etch rate vT (W; x) as a function of the depth x within the detector follow from vT (W; t) =
dL (W; t) + vB dt
(2)
substituting the variable t by the depth x according to x = L + vB t:
(3)
The bulk etch rate was vB = 1:83 m=h for the detector batch used for proton and alpha particle irradiation, whereas the detectors irradiated by deuterons and lithium ions are characterised by vB = 1:73 m=h. Since the normalised ratio V = vT =vB is used for the further evaluation, these small di'erences in vB do not play any role. The track etch rate vT (W; x) was determined for ions of di'erent kinds and initial
energy W . On the other hand, the restricted energy loss, REL350 (W; x), was computed as a function of W and x using the program StopPow (D,orschel and Henniger, 2000). By attaching vT (W; x) to REL350 (W; x) at the same values for W and x the function V = f (REL350 ) follows. The results are expected to agree approximately with the values resulting from the simple formula (1) if the track etch rate varies only slowly. This is the case for low-energy light ions only at the beginning of the etching process at a small depth below the detector surface. 3. Results Fig. 1 shows the etch-rate ratio determined as a function of REL350 for protons, alpha particles and lithium ions with a wide variety of the initial particle energy. Since the results for several energies are congruent, their discrimination by di'erent symbols is not recognisable in Fig. 1 in these cases. The data for deuterons were not added to the presentation for the purpose of clarity. They match the results for protons quite well as demonstrated in Fig. 2. The functions found for the etch-rate ratio along proton, deuteron and alpha-particle-induced tracks do not show any systematic dependence on the initial particle energy. The standard deviation (1) for V taking into account the whole data set at the corresponding REL350 value did not exceed 12%. This seems to be smaller than that expected from the visual impression on the width of variation in Figs. 1 and 2. However, as mentioned above, several points at a given REL350 value were congruent and their discrimination by di'erent symbols is not recognisable from the
B. D'orschel et al. / Radiation Measurements 35 (2002) 183 – 187
185
Fig. 1. Etch-rate ratio, V , as a function of restricted energy loss, REL350 , for protons, alpha particles and lithium ions of di'erent initial energies.
Fig. 2. Etch-rate ratio, V , as a function of restricted energy loss, REL350 , for protons and deuterons of di'erent initial energies. The line corresponds to the generalised curve from Fig. 1.
not be tested experimentally because the tracks were too short for the length measurement in these cases. Results for V (REL) were also presented by other authors who extracted the track etch rate from the track diameters after Eq. (1). A comparison of these results with the data given in Fig. 1 showed that the curves presented in the literature are more ;at (see e.g. Baiocchi et al., 1995). The reason for this e'ect is that vT following from Eq. (1) is depth-independent, whereas the vT values resulting from Eq. (2) increase with the depth and, therefore, with REL. An agreement of the results should, however, be expected for
REL350 at the detector surface. This corresponds to REL350 for the initial ion energy. Fig. 3 shows the results in comparison with the data published by other authors (Baiocchi et al., 1995) for protons and alpha particles as well as beryllium and silicon ions. The agreement is satisfying taking into account the experimental uncertainties. Furthermore, the results for lithium ions determined after Eqs. (1) and (2), respectively, were compared by con
186
B. D'orschel et al. / Radiation Measurements 35 (2002) 183 – 187
Fig. 3. Etch-rate ratio at the detector surface, V0 , as a function of the restricted energy loss, REL350 . The line corresponds to the results for protons, alpha particles and lithium ions with initial energies given in Fig. 1. The points represent data of Baiocchi et al. for ions with initial energies given at the corresponding site.
Fig. 4. Etch-rate ratio, V , as a function of restricted energy loss, REL350 , for lithium ions of di'erent initial energies. The REL350 values correspond to the region beyond the Bragg peak. The line characterises the results from Fig. 1 for REL350 values below the Bragg peak.
trajectory should, however, be extracted from the depthdependent track etch rate after Eqs. (2) and (3). In Figs. 1–3, the V (REL350 ) relationship is given for ions slowed-down up to the Bragg peak. The experimental determination of the depth-dependent track etch rate also allows, however, to extract etch-rate ratios for REL350 values beyond the Bragg peak. For this purpose vT (W; x) data are used for x values between the position of the maximum and that depth where vT drops to vB . Fig. 4 shows the results for lithium ions of di'erent initial energies. The curves coin-
cide with each other where the standard deviation at a given REL350 value does not exceed 16%. Besides, a good agreement with the generalised curve for V (REL350 ) derived from the results in Fig. 1 for REL350 values on the other side of the Bragg peak (using the 10:96 MeV 7 Li data) is observed. 4. Discussion and conclusions The etch-rate ratio found for protons, deuterons, alpha particles and 7 Li ions of di'erent energies can be correlated
B. D'orschel et al. / Radiation Measurements 35 (2002) 183 – 187
to the restricted energy loss resulting in a unique function V (REL350 ) within certain limits. The deviations observed for low-energy lithium ions at REL350 values corresponding to small depths within the detector seem to result from a reduced track etching at the beginning of the etching process. That means, the track etch rate is lower than expected. This e'ect is marked more distinctly for low ion energies where very-high track etch rates are obtained, whereas for higher ion energies the track etch reduction seems to play no role. Also, at greater depths within the detector this e'ect is not pronounced for the ions considered as demonstrated by the agreement in V (REL350 ) for REL350 values beyond the Bragg peak. A possible explanation could be that at high REL350 values near the detector surface, the track etch rate does not jump to the expected high values but a continuous increase occurs. This behaviour is more distinct the heavier the ion is. In the case of protons, deuterons and alpha particles it was not observed at the particle energies considered here but it cannot be excluded that it occurs likewise at lower energies. The main conclusion from these studies is, that a generalised V (REL350 ) relationship can be given for all the cases where the reduction of the track etch rate at the beginning of the etching process is only of little in;uence. Otherwise, the V (REL350 ) relationship has to be speci
187
Benton, E.V., Nix, W.D., 1969. The restricted energy loss criterion for registration of charged particles in plastics. Nucl. Instrum. Methods 67, 343–352. Doke, T., Hayashi, T., Nagaoka, S., Ogura, K., Takeuchi, R., 1995. Estimation of dose equivalent in STS-47 by a combination of TLDs and CR-39. Radiat. Meas. 24, 75–82. D,orschel, B., Bretschneider, R., Hermsdorf, D., Kadner, K., K,uhne, H., 1999. Measurement of the track etch rates along proton and alpha particle trajectories in CR-39 and calculation of the detection eBciency. Radiat. Meas. 31, 103–108. D,orschel, B., F,ulle, D., Hartmann, H., Hermsdorf, D., Kadner, K., Radlach, Ch., 1997. Measurement of track parameters and etch rates in proton-irradiated CR-39 detectors and simulation of neutron dosemeter responses. Radiat. Prot. Dosim. 69, 267–274. D,orschel, B., Henniger, J., 2000. The program StopPow—a useful tool for computation of energy loss and range of light ions in SSNTD’s. Nucl. Instrum. Methods (B) 171, 423–430. Fromm, M., Membrey, F., El Rahamany, Chambaudet, A., 1993. Principle of light ions micromapping and dosimetry using CR-39 polymeric detector: modelized and experimental uncertainties. Nucl. Tracks Radiat. Meas. 21, 357–365. G,unther, W., Leugner, D., Becker, E., Flesch, F., Heinrich, W., H,untrup, G., Reitz, G., R,ocher, H., Streibel, T., 1999. Energy spectrum of iron nuclei measured inside the MIR space craft using CR-39 track detectors. Radiat. Meas. 31, 585–590. Somogyi, G., 1980. Development of etched nuclear tracks. Nucl. Instrum. Methods 173, 21–42. Yadav, J.S., 1995. Charged particle identi