statistical analysis of stopping power of polymers … · statistical analysis of stopping power of...

STATISTICAL ANALYSIS OF STOPPING POWER OF POLYMERS

FOR HEAVY IONS

Mohan Singh*, Lakhwant Singh, Navjeet Kaur

Department of Physics, Guru Nanak Dev University, Amritsar, Punjab-143005, India

*e-mail: [email protected]

Abstract. This is a continuation of our earlier work (Radiation Effects & Defects in Solids, 163, No. 7, 2008, 605–623) for the up-to-date comparative study of various stopping power tables and codes for heavy ions ( 13 29Z ) in polymers using the statistical analyses in the

energy range ~ 0.19-3.14 MeV/n. The SRIM (Stopping and Range of Ions in Matter) and CasP (Convolution approximation for swift Particles) formulations are now updated and their new versions (SRIM2008.04 and CasP4.0) are available in the literature. Six different polymers mostly used as particle track detectors viz: Mylar (Polyethylene Terephthalate), PEN (Polyethylene Napthalate), Polycarbonate, CR-39 (Polyallyl Diglycol Carbonate), Kapton (Polypyromellitimide) and LR-115 (Cellulose Nitrate) have been chosen for this investigation. The merits and demerits of these adopted formulations are highlighted in the present paper. 1. Introduction The interaction of heavy ions with matter has become the area of intensive concentration both experimentally and theoretically [1-9]. Effective and successful applications of ion beam technology require detailed qualitative knowledge of different interaction processes. The stopping power or stopping force of any medium for different ions constitute information essential for ion-beam science and its applications. The interaction mechanism of energetic heavy ions with matter are well known at the present time, but no appropriate theoretical or semi-emperical formulations exist to calculate the stopping power of various materials for a variety of different isotopes with varying energies. Various analyses, developments, modifications and interests have continuously influenced the ideas for deep understanding of various complex interaction phenomena [2-16]. Some famous stopping power formulations (SRIM and CasP) have been modified and their new versions (SRIM2008.04 and CasP4.0) with various modifications are now avialable in the literature [12, 16]. For the study of heavy ions irradiated polymers and their successful applications, it seems therefore appropriate to present an up-to-date comparison of these formulations to judge their reliability, which will be helpful for scientific community.

As a continuation of our earlier work [9], the reliability of the modified versions of these formulations (SRIM2008.04 and CasP4.0) [12, 16] has been checked through the comparison of the computed values with the corresponding experimental data of stopping power of some important polymers for a variety of medium heavy ions ( 13 29Z ) in the

energy range ~0.19-3.14 MeV/n.

Materials Physics and Mechanics 11 (2011) 95-104 Received: April 07, 2011

© 2011, Institute of Problems of Mechanical Engineering

2. Present work In the present investigation, an up-to-date reliability of famous and avialable theoretical (CasP4.0) [16] and semi-empirical (SRIM2008.04) [12] procedures of stopping power calculation has been checked using the statistical analysis of deficits between computed and the experimental data of six important polymers [Mylar (Polyethylene Terephthalate), PEN (Polyethylene Napthalate), Polycarbonate, CR-39 (Polyallyl Diglycol Carbonate), Kapton (Polypyromellitimide) and LR-115 (Cellulose Nitrate)] for a variety of medium heavy ions ( 13 29Z ) in the energy range of ~0.19-3.14 MeV/n. The detail of experimental data [17-

25] used in this comparative analysis have already been discussed and presented in our last article [9]. Among the stopping power formulations used in previous work, new modifications in theoretical formulation (CasP) and semi-emperical (SRIM) have been implemented in their new versions (CasP4.0, SRIM2008.04) [12, 16].

In version 3.2 (CasP3.2) new modifications [improved relativistic correction accounted for the impact-parameter dependence, new projectile-electron loss (energy losses due to projectile ionization and excitation) option now also for compounds, new MEIS (Medium Energy Ion-Scattering) energy-loss parameter output] have been implemented. In CasP4.0, Modification on Bloch and Shell corrections are implemented, internal charge number for the UCA scaling for screened projectiles is improved, close collision function is replaced by an accurate fit formula, improved the accuracy for deeply bound inner shell by introducing new gridding, improved a model for the energy-loss spreading at b=0, the Barkas effect for close non-Coulombic collisions has been included, possible direct selection of the projectile charge-state is implemented and the speed of stopping cross-section calculations has also been improved.

Major changes occur in SRIM about every 5 years. In SRIM2006 one can now download the complete plots showing the experimental/theoretical stopping of any ion in any elemental target (it contains over 22,000 experimental data points reported since 1899), the error message "The number of recoils has exceeded SRIM memory" has been fixed, one can now make a file EXYZ.txt which shows the position of the incident ion at discrete energy points, one can now enter individual damage energies for each atom in each layer (this improves both damage calculations and sputtering calculations) for layered materials. The TRIM output window "SHOW LIVE DATA" has been improved.

In SRIM2008 many small bugs have been corrected, it is now possible to add range and damage spectra from different ions at different energies and angles into a single spectra, during the TRIM calculation, one can pause TRIM, and then change TRIM, has the option of adding the new data to the old data-files has been implemented. 3. Results and discussion

The energy behaviour of percentage deviation exp

exp100calS S

S

between the experimental and

the calculated stopping power values (using SRIM2008.04 and CasP4.0 codes) of six different polymers e.g. Mylar (Polyethylene Terephthalate, C10H8O4), PEN (Polyethylene Napthalate, C7H5O2), PC (Polycarbonate, C16H14O3), CR-39 (Polyallyl-Diglycol Carbonate, C12H18O7), Kapton (Polypyromellitimide, C22H18O5N2) and LR-115 (Cellulose Nitrate, C6H9O9N2) for a variety of projectiles ( 13 29Z ) having energy ranges of

~0.19−3.14MeV/n are shown in Figs. 1–6. For mylar (C10H8O4), it is clearly observed from Fig. 1(a,b) that the semi-empirical

SRIM2008.04 code produces stopping power values for a variety of heavy ions up-to maximum deficit of 10% [except 19% for Sc (0.36 MeV/n)] and CasP4.0 produces the values with an deficit of 20%. No any regular trend is observed among the energy behaviour of deviation shown by the values predicted by SRIM2008.04 code, but for CasP4.0 formulation

96 Mohan Singh, Lakhwant Singh, Navjeet Kaur

the % deviation decreases as the energy of the projectile increases. In many cases, the deviation shown by CasP4.0 increases as the energy of ions decreases. Figure 1b clears that the CasP4.0 give much less stopping power values as compared to the experimental data. It is interesting to note that for mylar/heavy ion combination, the SRIM2008.04 formulation by Ziegler [12] can give us much better results as compared to the theoretical formulation (CasP4.0) of Grande and Schiweitz [16].

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

-20

-15

-10

-5

0

5

10

Mylar, SRIM 2008.04

% D

evia

tion

Energy (MeV/n)

B C N O Na Al Si P S Cl Ar Sc Ti V Cr Mn Ni Cu

(a)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10 Mylar, CasP 4.0 B C N O Na Al Si P S Cl Ar Sc Ti V Cr Mn Ni Cu

% D

evia

tion

Energy (MeV/n)

(b)

Fig. 1. The percentage deviation of the stopping power values calculated using (a) SRIM2008.04 [12] and (b) CasP4.0 [16] codes from the experimental values [17-20, 22, 24] as a function of specific energy in Mylar (Polyethylene Terephthalate, C10H8O4) for various heavy ions in the energy range ~ 0.27–3.14MeV/n.

The new version of SRIM (SRIM2008.04) has no any new modified calculations as

compared to its earlier versions (SRIM2003.26). The CasP in its new version (CasP4.0)

97Statistical analysis of stopping power of polymers for heavy ions

predict significantly improved stopping power values as compared to its earlier version (CasP3.1) [9], but still it needs some more modifications in lower regions.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-15

-10

-5

0

5

10

15

PEN, SRIM 2008.04

% D

evia

tion

Energy (MeV/n)

C F Mg Al Si Sc V Cr Mn Ni Cu

(a)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

-24

-22

-20

-18

-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8PEN, CasP 4.0 C

F Mg Al Si Sc V Cr Mn Ni Cu

% D

evia

tion

Energy (MeV/n)

(b)

Fig. 2. The percentage deviation of the stopping power values calculated using (a) SRIM2008.04 [12] and (b) CasP4.0 [16] codes from the experimental values [25] as a function of specific energy in PEN (Polyethylene Napthalate, C7H5O2) for various heavy ions in the energy range ~ 0.19–3.10 MeV/n.

For PEN (Polyethylene Napthalate, C7H5O2), it is clear from Fig. 2(a,b) that the semi-

empirical formulation SRIM2008.04 produces stopping power values up-to maximum deficit of 8% [except 11% for C (3.10 MeV/n), 13% for F (0.85 MeV/n), 13% for Cr (0.48 MeV/n) and 14% for Cr (0.21 MeV/n)] and CasP4.0 produces the values with an deficit of 18% [except 23% for F (0.33 MeV/n)]. SRIM(2008.04) code predict the stopping power outputs with an error (% deviation) of ±6%. No any regular trend is observed among the energy


behaviour of deviation shown by the values predicted by SRIM2008.04 code but for CasP4.0 formulation, the % deviation decreases as the energy of the projectile increases in few cases. For Mg, V and Ni, SRIM2008.04 code give us maximum accurate stopping power values. CasP4.0 give better results for higher projectiles like Sc, V, Cr, Mn, Ni, Cu as compared to C, F, Mg, Al and Si etc. There is no largely modified outputs of new version of SRIM (SRIM2008.04) as compared to its earlier version (SRIM2003.26), but CasP4.0 produced much better stopping power results as compared to CasP3.1 [9]. These two adopted formulations calculate much less stopping power values as compared to the experimental data. For PEN/heavy ion combinations, we should prefer SRIM2008.04 code [12] for stopping power calculations.

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

Polycarbonate, SRIM 2008.04 C O F Mg Al Si Ar Sc V Cr Mn Ni Cu

% D

evia

tion

Energy (MeV/n) (a)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

-15

-10

-5

0

5

10Polycarbonate, CasP 4.0

C O F Mg Al Si Ar Sc V Cr Mn Ni Cu

% D

evia

tion

Energy (MeV/n) (b)

Fig. 3. The percentage deviation of the stopping power values calculated using (a) SRIM2008.04 [12] and (b) CasP4.0 [16] codes from the experimental values [23, 24] as a function of specific energy in PC (polycarbonate, C16H14O3) for various heavy ions in the energy range ~ 0.30–2.99 MeV/n.


From Fig. 3(a,b), it is clear that for PC (polycarbonate, C16H14O3) that the SRIM2008.04 code produces stopping power values for a variety of heavy ions up-to maximum deficit of 10% [except for Mg (14%) and Cu (13%)] and CasP4.0 code produces the values with an deficit of 13% [except 16% for Si (0.49MeV/n) projectile]. In this case the semi-empirical procedure SRIM2008.04 of Ziegler [12] can produce better results as compared to the theoretical formulation (CasP4.0) of Grande and Schiweitz [16].

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

CR-39, SRIM 2008.04

% D

evia

tion

Energy (MeV/n)

Li B C N O Na Al Si

(a)

0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8

-16

-15

-14

-13

-12

-11

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

CR-39, CasP 4.0

Li B C N O Na Al Si

% D

evia

tion

Energy (MeV/n) (b)

Fig. 4. The percentage deviation of the stopping power values calculated using (a) SRIM2008.04 [12] and (b) CasP4.0 [16] codes from the experimental values [19] as a function of specific energy in CR-39 (Polyallyl-Diglycol Carbonate, C12H18O7) for various heavy ions in the energy range ~ 0.372–2.596 MeV/n.

For CR-39 (Polyallyl-Diglycol Carbonate, C12H18O7) detector material, it is clear from

Fig. 4(a,b) that semi-empirical formulation SRIM2008.04 produces stopping power values for


a variety of heavy ions up-to maximum deficit of 8% and CasP4.0 produces the values with an deficit of 15%. For Li projectile, the CasP4.0 give better results as compared to other chosen ions. The deviation shown by CasP4.0 increases as the energy of ions decreases. The values predicted by the theoretical procedure (CasP4.0) become more deviated for heavy projectile (like Na, Al and Si) as compared to other light ions but SRIM2008.04 give better results for heavy projectiles. In this case, the semi-empirical procedure SRIM2008.04 of Ziegler [12] can produce reliable stopping power values as compared to the theoretical formulation (CasP4.0) of Grande and Schiweitz [16].

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

4.5

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

10.5

11.0

11.5

12.0

12.5

Kapton, SRIM 2008.04

% D

evia

tion

Energy (MeV/n)

B C N O

(a)

0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

-9

-8

-7

-6

-5

-4

Kapton, CasP 4.0

B C N O%

Dev

iati

on

Energy (MeV/n) (b)

Fig. 5. The percentage deviation of the stopping power values calculated using

(a) SRIM2008.04 [12] and (b) CasP4.0 [16] codes from the experimental values [17, 18, 20] as a function of specific energy in Kapton (Polypyromellitimide, C22H18O5N2) for various heavy ions in the energy range ~ 0.63–1.96 MeV/n.


From Fig. 5(a,b), it is clearly observed that for Kapton (Polypyromellitimide, C22H18O5N2), the SRIM2008.04 code produces stopping power values for a variety of heavy ions up-to maximum deficit of 12% and CasP4.0 produces the values with an deficit of 9%. The new versions of CasP4.0 formulation produces more accurate values as comapred to its earliar version [10] but new version of SRIM (SRIM2008.04) give us more deviated stopping power values as comapred to SRIM2003.26. In this case the theoretical formulation (CasP4.0) of Grande and Schiweitz [16] can produce better stopping power values as compared to the semi-empirical procedure SRIM2008.04 of Ziegler [12].

0.5 1.0 1.5 2.0 2.5

-3

-2

-1

0

1

2

3

4

5

6LR-115, SRIM 2008.04

% D

evia

tion

Energy (MeV/n)

Li B C N O

(a)

0.5 1.0 1.5 2.0 2.5-18

-16

-14

-12

-10

-8

-6

-4

-2

0

LR-115, CasP 4.0

Li B C N O

% D

evia

tion

Energy (MeV/n) (b)

Fig. 6. The percentage deviation of the stopping power values calculated using

(a) SRIM2008.04 [12] and (b) CasP4.0 [16] codes from the experimental values [21] as a function of specific energy in LR-115 (Cellulose Nitrate, C6H9O9N2) for various heavy ions in the energy range ~ 0.513–2.446 MeV/n.


For LR-115 (Cellulose Nitrate, C6H9O9N2), it is clear from Fig. 6 that semi-empirical formulation SRIM2008.04 produces stopping power results with maximum deficit of 5% and CasP4.0 produces the values with an deficit of 14%. In some cases, SRIM2008.04 tabulated stopping power values with zero percent error. All values given by theoretical formulatiion CasP4.0 are much less as compared to the experimental data. As the energy of the projectile decreases the stopping power values predicted by CasP4.0 become more deviate from the experimental data. In this case of cellulose nitrate, the semi-empirical procedure SRIM2008.04 of Ziegler [12] can produce reliable stopping power values as compared to the theoretical formulation (CasP4.0) of Grande and Schiweitz [16]. 4. Conclusion The knowledge of up-to-date reliability of different versions of various range and stopping procedures play a significant role in ion-beam science. The semi-empirical formulation (SRIM2008.04) of Ziegler give very reliable and accurate results of stopping power for various heavy projectiles/polymers combinations. The new versions of SRIM have no any big modifications in its stopping power calculations as compared to SRIM2003. The theoretical formulation (CasP) is improving its calculations time-to-time very well, but still it need some important modifications at lower energy regions. Acknowledgment One of the authors (M. Singh) is thankful to the Council of Scientific and Industrial Research (CSIR, India) for Research Associateship.

References

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statistical analysis of stopping power of polymers … · statistical analysis of stopping power of...

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