- Email: [email protected]
Bulk response of some polymeric nuclear track detectors to ionizing radiation
Nuclear Instruments and Methods 212 (1983) 371-373 North-Holland Publishing Company
BULK RESPONSE OF SOME TO IONIZING RADIATION
POLYMERIC
371
NUCLEAR
TRACK DETECTORS
H.B. LOCK
Akademie der Wissenschaftender DDR, Zentralinstitutfiir Kernforschung, Rossendorf/Dresden, DDR Received 24 August 1982
Response functions for bulk etching after electron or gamma irradiations are presented for Daicel, CR-39, PC and PETP. All response functions derived from available experimental data consist of a linear and one supralinear term. Based on the assumption that polymer chains are preferentially degraded from the chain ends the linear term can be explained in terms of a radiation induced growth in the surface concentration of chain ends. The supralinear term is supposed to be caused by the etching mechanism which is responsible for enhanced particle track etching as well.
1. Introduction
Studies of the bulk response of plastics to ionizing radiation can be valuable to applied nuclear physics particularly for the following aspects. The dose d e p e n d e n c e of the surface etch rate of some plastics c o m m o n l y ued as polymeric nuclear track detectors ( P N T D ) can be exploited for high exposure g a m m a dosimetry [1-4]. Exposure to high-energy electrons, gamma-rays or X-rays in the presence of oxygen after irradiation with heavy particles accelerates selectively the track etch rate v t in polyethyleneterephthalate [5] and p o l y c a r b o n a t e [6], which is of particular interest for the p r o d u c t i o n of nuclear track microfilters. A t t e m p t s have been m a d e to enlighten particle track response of P N T D in terms of their bulk response to electrons and gamma-rays [7-10]. In all the applications m e n t i o n e d above knowledge of a response function (RF) would be valuable but in the latter case it is of particular concern. In spite of this n o a t t e m p t has been reported to o b t a i n the R F for bulk response. Only for a very restricted dose range Varnagy et al. [3,4] published a relation for the dose d e p e n d e n c e of the normalized etch rate. Therefore the aim of this paper is to obtain the R F s for bulk response from experimental data which are a b u n d a n t in the literature. The derived RFs will be discussed a n d c o m p a r e d with the response in particle track etching. 2. The response functions
The experimental data concerning the surface etch rate e n h a n c e m e n t after a bulk irradiation with electrons 0167-5087/83/0000
0000/$03.00 © 1983 N o r t h - H o l l a n d
or gamma-rays were transformed into the normalized etch rate e n h a n c e m e n t (VD/Vs)--1, where v D is the surface etch rate after irradiation a n d vs is the etch rate of the unirradiated surface. The data for Daicel cellulose nitrate (CN), poly-allyl-diglycol-carbonate (Cr39), p o l y c a r b o n a t e (PC) a n d polyethyleneterephthalate (PETP) were compiled from refs. 1,2,7,11. In every case the dose d e p e n d e n c e of (VD/Vs)-- 1 shown in fig. 1 can be well described by a R F which consists of a linear and one supralinear term, 1) D / I ) S =
1 + aiD + a,,D n,
(1)
103
102
"~'~ 101' ~ i !
10or /
[ 10 0
<
/ 101
, 102
103
104
e Nrad] Fig. 1. Bulk response of some polymers used as PNTD. The experimental points were compiled from refs. 1,2,7,11. The curves were calculated from eq. (1) with the coefficients given in table 1.
372
H.B. Lack / Bulk response of track detectors
Table 1 Coefficients a, for the RFs of the curves given in fig. 1. The RFs have the form of eq. (1). Material
Radiation
Etchant
aI
(CR-39) 1 (Homalite) (CR-39)2 (Homalite) CN (Daicel) PC~ (Lexan)
e
20% NaOH 343 K 20% NaOH 313 K 10 M NaOH 298 K 6.25 N NaOH 0.5% Benax 343.4 K 30% KOH 343 K 30% KOH 343 K
2.0x10
PC 2 (Makrofol E) PETP (Melinex)
e y -y
ee
a2
a3
a4
Ref.
i
_
6.5×10 7
[11]
8.0×10 2
_
6.7×10 s
[11]
2.9×10 2
3.9x 10-3
_
[1]
3.5 x 10 3
_
2.8x 10- s
[2]
7.8×10 3
_
_
7.3×10
12
[7]
3.4×10 3
_
_
1.0×10 ~3
[7]
where D is the dose in Mrad. The curves in fig. 1 were calculated using eq. (1) with the coefficients displayed in table 1. A distinguishing feature of the RFs for bulk response is the appearance of the linear term. In particle track etching a linear term was only found for CR-39 [12]. 3. Discussion of the RFs for bulk response Although a comprehensive theory about the response of polymers to ionizing radiation is not yet available [13,14], there is some evidence that in the dose range considered here a linear correlation exists between the yield of primary activations and the a b s o r b e d dose [15,16]. This assumption is supported by the well established effect of energy transfer in polymer chains which can be thought of as the reason for the fact that only one radical type is produced in almost every irradiated polymer [8,13,14]. In addition, energy transfer is responsible for improved radiation resistance of aliphatic polymers onto which aromatic groups have been grafted [17]. Consequently, no exponential dose dependence is employed in eq. (1), although Varnagy et al. [3,4] reported that the dose dependence of v D / v S can be well described by an exponential function in a restricted dose range. The appearance of a supralinear term does not confirm a multi-hit response in the formation of the reactive species in the polymer. The supralinear term is rather a result of the etching mechanism as will be discussed later. The linear term in the R F for bulk response can be explained in terms of a linear increase of the chain end concentration at the surface with dose. If the chemical etching is restricted to the surface which is most likely
for CR-39, PC and PETP [18] it can be assumed that the polymer chains are preferentially degraded from the chain ends accessible at the surface. The appearance of one supralinear term with different exponents can be understood in terms of the model of free reaction volume which is based on the assumption that for chain cleavage within the bulk a free volume is required to enable the attack of the etchant a n d to form the activated complex [16]. In this mode the degradation is no longer restricted to the surface but etching proceeds in a layer of constant thickness after an induction period. In analogy to particle track etching the exponent of the supralinear term in eq. (1) represents the ratio V*/V~, where V* is the required free reaction volume a n d Vf is the free volume of a hole generated by release of a gaseous radiolysis product [16]. The variation of the exponent observed even for the same material appeared to be caused by an alteration in the hole density [19]. A reduction of the original hole density can be induced for example, by structural changes above the glass transition temperature Tg. On the other h a n d the hole density can be increased by photo-oxidative degradation. A deviation from eq. (1) can be expected when a surface layer is built up from reaction products or plasticizers which have a low solubility in the etchant. The diffusion resistance of such a layer diminishes the %tch rate. This is the case for CR-39 where v D becomes lower than the predicted value at a dose of a b o u t 150 200 M r a d (fig. 1). It can be assumed that the diffusion layer is formed from poly(allyl alcohol) which is a polymeric etch product of CR-39 with a limited solubility in the etchant [20]. In the case of Daicel the plasticizer c a m p h o r is responsible for the decreasing slope of the response curve at a dose of a b o u t 100 M r a d [71.
H.B. Liick / Bulk response of track detectors
4. Comparison to track response A characteristic feature of the RFs o b t a i n e d for particle track etching in CN, PC a n d P E T P [19,21,22] is the absence of a linear term. Even for very low values of ( v t / v s ) - 1 there is no trend to turn to a linear correlation. The only exception is CR-39. The linear term in the R F of CR-39 [12,23] is perhaps a result of the rigid crosslinked polymer structure which m a y enable an accumulation of i n f o r m a t i o n a b o u t the location of chain ends along the particle trajectory, even if the degradation is restricted to the surface. A comparison of the e x p o n e n t of the supralinear term in bulk response with the e x p o n e n t of the R F in track response reveals a substantial analogy. As mentioned above the e x p o n e n t in b o t h R F s are considered to represent the ratio V * / V f . As reported in a previous p a p e r [19] the e x p o n e n t of the R F for particle track etching in C N was found to vary from 2 to 5 for different etching conditions. H e n c e the m a x i m u m difference in the exponents of the R F s for bulk a n d track response which is one for CR-39, PC and P E T P [21-23] c a n be explained in terms of different e n v i r o n m e n t a l conditions. It should be n o t e d that the exponent is only slightly influenced by the model used for calculating t h a t fraction of particle energy which is relevant to preferential track etching [24]. In analogy to bulk etching at a high etch rate ratio a levelling off can be expected for the response curve in particle track etching in a plasticized P N T D . U p to an etch rate ratio of a b o u t 6 0 - 8 0 no deviation was rep o r t e d for CR-39 [12,25,26]. On the other h a n d it was f o u n d for PETP that the exponent turns from 3 to 1 with increasing track etch rate. The effect is more p r o n o u n c e d in a c o n c e n t r a t e d etchant [27]. Therefore it is necessary in every case to ensure that the response curve is not affected by diffusion processes in the etchant or through a layer of etch products.
5. Conclusion The present findings suggest that only the supralinear term of the R F for bulk response should serve for a comparison with the supralinear term of the R F for particle response. A precondition for a reasonable comparison is that the response data were o b t a i n e d for the same storage and etching conditions. But even when etching was performed at a given temperature different exponents may be found for the R F s of bulk a n d track response for various reasons. F o r example, in track response the loss of holes by diffusion into the bulk is governed by the t e m p e r a t u r e difference to the glass transition t e m p e r a t u r e Tg of the u n d a m a g e d bulk
373
material, while in a bulk irradiated polymer the holes are mainly lost by relaxation of the damaged polymer structure which has generally a lower Tg. Both bulk response a n d particle track etching in P N T D involve a sequence of interlocking chemical reactions which are influenced by the material parameters a n d e n v i r o n m e n t a l conditions. Keeping this in m i n d results o b t a i n e d for bulk response can be used in addition to enlighten the m e c h a n i s m of particle track formation and etching.
References [l] E.V. Benton, NRDL-TR-68-14 (1968). [2] A.L. Frank and E.V. Benton, Rad. Effects 2 (1970) 269. [3] M. Varnagy, J. Csikai and S. Szegedi, Nucl. Instr. and Meth. 119 (1974) 261. [4] M. Varnagy, Nucl. Instr. and Meth. 152 (1978) 591. [5] S.P. Tretyakova and T.I. Mamonova, Dubna Report 1411439 (1978). [6] W. DeSorbo, Nucl. Tracks 3 (1979) 13. [7] B. Schlenk, G. Somogyi and A. Valek, Rad. Effects 24 (1975) 247. [8] A. Chambaudet and J. Roncin, Proc. l l t h Int. Conf. on Solid state nuclear track detectors, Bristol (1981). [9] E.A. Edmonds and S.A. Durrani, Nucl. Tracks 3 (1979) 3. [10] M. Zamani and S. Charalambous, Nucl. Tracks 4 (1980) 177. [11] G. Somogyi, Proc. llth Int. Conf, on Solid state nuclear track detectors, Bristol (1981). [12] H.B. Li~ck, Rad. Effects Lett. 67 (1982) 141. [13] R.S. Alger, Radiation effects in polymers, in Physics and chemistry of the organic solid state, ed., D. Fox (Intersci. Publ., New York and London, 1965). [14] M. Dole (ed.), The radiation chemistry of macromolecules, vols. I and II (Academic Press, New York, 1972/1973). [15] H.G. Paretzke, Proc. 1 lth Int. Conf. on Solid state nuclear track detectors, Bristol (1981). [16] H.B. Ltick, Nucl. Instr. and Meth. 202 (1982) 497. [17] J.C. Arthur Jr., D.J. Stanonis, T. Mares and O. Hinojosa, J. Appl. Polym. Sci. 11 (1967) 1129. [18] H.B. Ltick, Nucl. Instr. and Meth. 200 (1982) 517. [19] H.B. Liick, Nucl. Instr. and Meth. 212 (1983) 483. [20] T.A. Gruhn, W,K. Li, E.V. Benton, R.M. Cassou and C.S. Johnson, Proc. 10th Int. Conf. on Solid state nuclear track detectors, Lyon (1979) p, 291. [21] G. Somogyi, K. Grabisch, R. Scherzer and W. Enge, Nucl. Instr. and Meth. 134 (1976) 129. [22] H.B. Liick, Isotopenpraxis 14 (1978) 215. [23] H.B. Ltick, Nucl. Instr. and Meth. 198 (1982) 611. [24] H.B. Ltick and G. Pretzsch, to be published. [25] P.H. Fowler, V.M. Clapham and D.L. Henshaw, Proc. 10th Int. Conf. on Solid state nuclear track detectors, Lyon (1979) p. 437. [26] D.L. Henshaw, N. Griffith, O.A.L. Landen and E.V. Benton, Nucl. Instr. and Meth. 180 (1981) 65. [27] H.B. Liick, Nucl. Instr. and Meth., to be published.
BULK RESPONSE OF SOME TO IONIZING RADIATION
POLYMERIC
371
NUCLEAR
TRACK DETECTORS
H.B. LOCK
Akademie der Wissenschaftender DDR, Zentralinstitutfiir Kernforschung, Rossendorf/Dresden, DDR Received 24 August 1982
Response functions for bulk etching after electron or gamma irradiations are presented for Daicel, CR-39, PC and PETP. All response functions derived from available experimental data consist of a linear and one supralinear term. Based on the assumption that polymer chains are preferentially degraded from the chain ends the linear term can be explained in terms of a radiation induced growth in the surface concentration of chain ends. The supralinear term is supposed to be caused by the etching mechanism which is responsible for enhanced particle track etching as well.
1. Introduction
Studies of the bulk response of plastics to ionizing radiation can be valuable to applied nuclear physics particularly for the following aspects. The dose d e p e n d e n c e of the surface etch rate of some plastics c o m m o n l y ued as polymeric nuclear track detectors ( P N T D ) can be exploited for high exposure g a m m a dosimetry [1-4]. Exposure to high-energy electrons, gamma-rays or X-rays in the presence of oxygen after irradiation with heavy particles accelerates selectively the track etch rate v t in polyethyleneterephthalate [5] and p o l y c a r b o n a t e [6], which is of particular interest for the p r o d u c t i o n of nuclear track microfilters. A t t e m p t s have been m a d e to enlighten particle track response of P N T D in terms of their bulk response to electrons and gamma-rays [7-10]. In all the applications m e n t i o n e d above knowledge of a response function (RF) would be valuable but in the latter case it is of particular concern. In spite of this n o a t t e m p t has been reported to o b t a i n the R F for bulk response. Only for a very restricted dose range Varnagy et al. [3,4] published a relation for the dose d e p e n d e n c e of the normalized etch rate. Therefore the aim of this paper is to obtain the R F s for bulk response from experimental data which are a b u n d a n t in the literature. The derived RFs will be discussed a n d c o m p a r e d with the response in particle track etching. 2. The response functions
The experimental data concerning the surface etch rate e n h a n c e m e n t after a bulk irradiation with electrons 0167-5087/83/0000
0000/$03.00 © 1983 N o r t h - H o l l a n d
or gamma-rays were transformed into the normalized etch rate e n h a n c e m e n t (VD/Vs)--1, where v D is the surface etch rate after irradiation a n d vs is the etch rate of the unirradiated surface. The data for Daicel cellulose nitrate (CN), poly-allyl-diglycol-carbonate (Cr39), p o l y c a r b o n a t e (PC) a n d polyethyleneterephthalate (PETP) were compiled from refs. 1,2,7,11. In every case the dose d e p e n d e n c e of (VD/Vs)-- 1 shown in fig. 1 can be well described by a R F which consists of a linear and one supralinear term, 1) D / I ) S =
1 + aiD + a,,D n,
(1)
103
102
"~'~ 101' ~ i !
10or /
[ 10 0
<
/ 101
, 102
103
104
e Nrad] Fig. 1. Bulk response of some polymers used as PNTD. The experimental points were compiled from refs. 1,2,7,11. The curves were calculated from eq. (1) with the coefficients given in table 1.
372
H.B. Lack / Bulk response of track detectors
Table 1 Coefficients a, for the RFs of the curves given in fig. 1. The RFs have the form of eq. (1). Material
Radiation
Etchant
aI
(CR-39) 1 (Homalite) (CR-39)2 (Homalite) CN (Daicel) PC~ (Lexan)
e
20% NaOH 343 K 20% NaOH 313 K 10 M NaOH 298 K 6.25 N NaOH 0.5% Benax 343.4 K 30% KOH 343 K 30% KOH 343 K
2.0x10
PC 2 (Makrofol E) PETP (Melinex)
e y -y
ee
a2
a3
a4
Ref.
i
_
6.5×10 7
[11]
8.0×10 2
_
6.7×10 s
[11]
2.9×10 2
3.9x 10-3
_
[1]
3.5 x 10 3
_
2.8x 10- s
[2]
7.8×10 3
_
_
7.3×10
12
[7]
3.4×10 3
_
_
1.0×10 ~3
[7]
where D is the dose in Mrad. The curves in fig. 1 were calculated using eq. (1) with the coefficients displayed in table 1. A distinguishing feature of the RFs for bulk response is the appearance of the linear term. In particle track etching a linear term was only found for CR-39 [12]. 3. Discussion of the RFs for bulk response Although a comprehensive theory about the response of polymers to ionizing radiation is not yet available [13,14], there is some evidence that in the dose range considered here a linear correlation exists between the yield of primary activations and the a b s o r b e d dose [15,16]. This assumption is supported by the well established effect of energy transfer in polymer chains which can be thought of as the reason for the fact that only one radical type is produced in almost every irradiated polymer [8,13,14]. In addition, energy transfer is responsible for improved radiation resistance of aliphatic polymers onto which aromatic groups have been grafted [17]. Consequently, no exponential dose dependence is employed in eq. (1), although Varnagy et al. [3,4] reported that the dose dependence of v D / v S can be well described by an exponential function in a restricted dose range. The appearance of a supralinear term does not confirm a multi-hit response in the formation of the reactive species in the polymer. The supralinear term is rather a result of the etching mechanism as will be discussed later. The linear term in the R F for bulk response can be explained in terms of a linear increase of the chain end concentration at the surface with dose. If the chemical etching is restricted to the surface which is most likely
for CR-39, PC and PETP [18] it can be assumed that the polymer chains are preferentially degraded from the chain ends accessible at the surface. The appearance of one supralinear term with different exponents can be understood in terms of the model of free reaction volume which is based on the assumption that for chain cleavage within the bulk a free volume is required to enable the attack of the etchant a n d to form the activated complex [16]. In this mode the degradation is no longer restricted to the surface but etching proceeds in a layer of constant thickness after an induction period. In analogy to particle track etching the exponent of the supralinear term in eq. (1) represents the ratio V*/V~, where V* is the required free reaction volume a n d Vf is the free volume of a hole generated by release of a gaseous radiolysis product [16]. The variation of the exponent observed even for the same material appeared to be caused by an alteration in the hole density [19]. A reduction of the original hole density can be induced for example, by structural changes above the glass transition temperature Tg. On the other h a n d the hole density can be increased by photo-oxidative degradation. A deviation from eq. (1) can be expected when a surface layer is built up from reaction products or plasticizers which have a low solubility in the etchant. The diffusion resistance of such a layer diminishes the %tch rate. This is the case for CR-39 where v D becomes lower than the predicted value at a dose of a b o u t 150 200 M r a d (fig. 1). It can be assumed that the diffusion layer is formed from poly(allyl alcohol) which is a polymeric etch product of CR-39 with a limited solubility in the etchant [20]. In the case of Daicel the plasticizer c a m p h o r is responsible for the decreasing slope of the response curve at a dose of a b o u t 100 M r a d [71.
H.B. Liick / Bulk response of track detectors
4. Comparison to track response A characteristic feature of the RFs o b t a i n e d for particle track etching in CN, PC a n d P E T P [19,21,22] is the absence of a linear term. Even for very low values of ( v t / v s ) - 1 there is no trend to turn to a linear correlation. The only exception is CR-39. The linear term in the R F of CR-39 [12,23] is perhaps a result of the rigid crosslinked polymer structure which m a y enable an accumulation of i n f o r m a t i o n a b o u t the location of chain ends along the particle trajectory, even if the degradation is restricted to the surface. A comparison of the e x p o n e n t of the supralinear term in bulk response with the e x p o n e n t of the R F in track response reveals a substantial analogy. As mentioned above the e x p o n e n t in b o t h R F s are considered to represent the ratio V * / V f . As reported in a previous p a p e r [19] the e x p o n e n t of the R F for particle track etching in C N was found to vary from 2 to 5 for different etching conditions. H e n c e the m a x i m u m difference in the exponents of the R F s for bulk a n d track response which is one for CR-39, PC and P E T P [21-23] c a n be explained in terms of different e n v i r o n m e n t a l conditions. It should be n o t e d that the exponent is only slightly influenced by the model used for calculating t h a t fraction of particle energy which is relevant to preferential track etching [24]. In analogy to bulk etching at a high etch rate ratio a levelling off can be expected for the response curve in particle track etching in a plasticized P N T D . U p to an etch rate ratio of a b o u t 6 0 - 8 0 no deviation was rep o r t e d for CR-39 [12,25,26]. On the other h a n d it was f o u n d for PETP that the exponent turns from 3 to 1 with increasing track etch rate. The effect is more p r o n o u n c e d in a c o n c e n t r a t e d etchant [27]. Therefore it is necessary in every case to ensure that the response curve is not affected by diffusion processes in the etchant or through a layer of etch products.
5. Conclusion The present findings suggest that only the supralinear term of the R F for bulk response should serve for a comparison with the supralinear term of the R F for particle response. A precondition for a reasonable comparison is that the response data were o b t a i n e d for the same storage and etching conditions. But even when etching was performed at a given temperature different exponents may be found for the R F s of bulk a n d track response for various reasons. F o r example, in track response the loss of holes by diffusion into the bulk is governed by the t e m p e r a t u r e difference to the glass transition t e m p e r a t u r e Tg of the u n d a m a g e d bulk
373
material, while in a bulk irradiated polymer the holes are mainly lost by relaxation of the damaged polymer structure which has generally a lower Tg. Both bulk response a n d particle track etching in P N T D involve a sequence of interlocking chemical reactions which are influenced by the material parameters a n d e n v i r o n m e n t a l conditions. Keeping this in m i n d results o b t a i n e d for bulk response can be used in addition to enlighten the m e c h a n i s m of particle track formation and etching.
References [l] E.V. Benton, NRDL-TR-68-14 (1968). [2] A.L. Frank and E.V. Benton, Rad. Effects 2 (1970) 269. [3] M. Varnagy, J. Csikai and S. Szegedi, Nucl. Instr. and Meth. 119 (1974) 261. [4] M. Varnagy, Nucl. Instr. and Meth. 152 (1978) 591. [5] S.P. Tretyakova and T.I. Mamonova, Dubna Report 1411439 (1978). [6] W. DeSorbo, Nucl. Tracks 3 (1979) 13. [7] B. Schlenk, G. Somogyi and A. Valek, Rad. Effects 24 (1975) 247. [8] A. Chambaudet and J. Roncin, Proc. l l t h Int. Conf. on Solid state nuclear track detectors, Bristol (1981). [9] E.A. Edmonds and S.A. Durrani, Nucl. Tracks 3 (1979) 3. [10] M. Zamani and S. Charalambous, Nucl. Tracks 4 (1980) 177. [11] G. Somogyi, Proc. llth Int. Conf, on Solid state nuclear track detectors, Bristol (1981). [12] H.B. Li~ck, Rad. Effects Lett. 67 (1982) 141. [13] R.S. Alger, Radiation effects in polymers, in Physics and chemistry of the organic solid state, ed., D. Fox (Intersci. Publ., New York and London, 1965). [14] M. Dole (ed.), The radiation chemistry of macromolecules, vols. I and II (Academic Press, New York, 1972/1973). [15] H.G. Paretzke, Proc. 1 lth Int. Conf. on Solid state nuclear track detectors, Bristol (1981). [16] H.B. Ltick, Nucl. Instr. and Meth. 202 (1982) 497. [17] J.C. Arthur Jr., D.J. Stanonis, T. Mares and O. Hinojosa, J. Appl. Polym. Sci. 11 (1967) 1129. [18] H.B. Ltick, Nucl. Instr. and Meth. 200 (1982) 517. [19] H.B. Liick, Nucl. Instr. and Meth. 212 (1983) 483. [20] T.A. Gruhn, W,K. Li, E.V. Benton, R.M. Cassou and C.S. Johnson, Proc. 10th Int. Conf. on Solid state nuclear track detectors, Lyon (1979) p, 291. [21] G. Somogyi, K. Grabisch, R. Scherzer and W. Enge, Nucl. Instr. and Meth. 134 (1976) 129. [22] H.B. Liick, Isotopenpraxis 14 (1978) 215. [23] H.B. Ltick, Nucl. Instr. and Meth. 198 (1982) 611. [24] H.B. Ltick and G. Pretzsch, to be published. [25] P.H. Fowler, V.M. Clapham and D.L. Henshaw, Proc. 10th Int. Conf. on Solid state nuclear track detectors, Lyon (1979) p. 437. [26] D.L. Henshaw, N. Griffith, O.A.L. Landen and E.V. Benton, Nucl. Instr. and Meth. 180 (1981) 65. [27] H.B. Liick, Nucl. Instr. and Meth., to be published.