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Heavy ion range anisotropy in muscovite mica
Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
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Heavy ion range anisotropy in muscovite mica Mohan Singh, Navjeet Kaur, Lakhwant Singh * Department of Physics, Guru Nanak Dev University, Amritsar, Punjab-143005, India
a r t i c l e
i n f o
Article history: Received 26 November 2009 Received in revised form 11 June 2010 Available online 1 July 2010 Keywords: Muscovite mica Layered crystal Heavy ions Stopping processes Anisotropy
a b s t r a c t The anisotropy of heavy ion range in layered crystal of muscovite mica has been studied in the present investigation. The freshly cleaved basal plane of the natural muscovite mica has been irradiated with various energetic heavy ions with different dip angles from UNILAC (Universal Linear Accelerator) heavy ion accelerator, GSI, Darmstadt, Germany. We have tried to investigate the causes and effects of the anisotropic nature of the layered crystalline mica on heavy ions propagation. The measured and available range values of number of heavy ions [viz: 58Ni; 93Nb; 129Xe; 132Xe; 197Au; 208Pb; 209Bi; and 238U] in muscovite mica are used to highlight the shortcomings of various range and energy loss formulations about the orientation effect on stopping processes in anisotropic media. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Because of the great importance and interest, the field of ion matter interaction explores many unique and diverse applications in various fields of science and technology. These interests and applications require a complete experimental and theoretical study of the irradiated materials for deep understanding of the different processes involved during the ions propagation [1–12]. The progress in accelerator technology and availability of a variety of beams of varying energy, masses and charge, availability of special type of radiation detectors, advanced instruments and development of new computational methods have led to several new demands in this field of science. In order to understand the mechanism of ion stopping, enormous work has been done on both theoretical and experimental sides. However, despite extensive research over almost a century, several central problems (incomplete knowledge of stopping processes) remain unsolved. It is important to find the solution of these problems and develop new ideas in experiments and theories. The interest for the complete knowledge about the basic fundamental processes responsible for the slowing down of energetic heavy ions in anisotropic material remains alive. Because of the complexities involved in the structures of these types of layered crystalline materials, various processes during ion penetration behave completely different from their amorphous counterparts. The layered crystalline structure has a large effect on the range and stopping of projectiles [7]. Various theoretical and semi-empirical formulations are present to study the ion stopping processes
* Corresponding author. Tel.: +91 183 2450926; fax: +91 183 2258820. E-mail address: [email protected] (L. Singh). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.06.024
[6,13–21], but there is no satisfactory treatment to provide a quantitative understanding of the phenomena involved in anisotropic media. Among various radiation detecting materials, the minerals (e.g., Mica) provide unique opportunity to measure the radiation effects and defects because of the better measurement of damage [7,22– 26]. The irradiated mica can provide enormous important applications in science and technology. Due to this, there is a dire need of studying various heavy ion stopping processes in it. In the present work, the anisotropic nature of layered crystal of muscovite mica has been investigated by studying the dip angle dependence of heavy ions ranges. We have tried to investigate the causes and effects of the anisotropic nature of the muscovite mica on heavy ions ranges. Various famous and available range formulations [SRIM, LISE++:0-[Hub90], LISE++:1-[Zie85], LISE++:8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (without LS correction)] [17,20] have been used to check their reliability about the orientation effect on the heavy ions range calculations. 2. Muscovite mica Minerals consist of negatively charge silicate layers bonded together by interlayer cations. Mica belongs to a family of minerals known as phyllosilicates. It has a monoclinic structure with unit structure consisting of one octahedral sheet sandwiching between two opposing tetrahedral sheets. It crystallizes in a layered structure and can be cleaved relatively easily into thin translucent sheets. These sheets form a layer that is separated from adjacent layers by planes of non-hydrated interlayer cations. In the present investigation, natural muscovite mica (q = 2.80 gm/cm3; crystallographic system: monoclinic [22,27–29]) was
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M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
Table 1 Electron-microprobe data for muscovite mica. Oxide
Weight%
Element
Weight%
Na2O MgO Al2O3 SiO2 K2O TiO2 FeO MnO Total H2O(assumed)
0.68 0.16 35.17 47.00 10.49 0.02 2.29 0.03 95.84 4.16
Na Mg Al Si K Ti Fe Mn O Total
0.51 0.10 18.61 21.96 8.70 0.01 1.78 0.03 44.13 95.84
collected from Nilore Mica belt, India. The chemical compositional analysis of the ‘‘as received” sample was carried out using the Electron Probe Microanalyser at IIT Roorkee, India. The results of the microprobe analysis are listed in Table 1. The structural formula of the muscovite mica calculated on the basis of EPMA is (K0.87 Na0.08)R0.95(Al1.98Mg0.02)R2.00 (Al0:72 Fe3þ 0:25 Si3:06 )R4.03O10(OH)1.81. Muscovite mica has layered structure consisting of series of sheets stacked parallel to each other [7]. It consists of infinite sheets of corner-shared SiO4 tetrahedra, with the apical oxygen atoms located at the corners of a hexagon. In this structure, onefourth of the Si is replaced by Al, with the remaining K+ and Al3+ ions lying in between the aluminosilicate sheets. A single octahedral AlO6 sheet is sandwiched between two tetrahedral SiO4 sheets, with a layer of K+ ions located between the trilayer aluminosilicate sheets (Fig. 1). Since the ionic bonding between the K+ layers and the trilayer aluminosilicate sheet is weak, mica cleaves rather easily at the positions of the K+ layers. The most stable surface [0 0 1] was used for heavy ion irradiation after cleaving the muscovite crystal [7,24].
3. Methodology In order to understand the orientation effect of layered crystalline materials on heavy ion stopping processes, the experimental range data for a variety of heavy ions [viz: 58Ni; 93Nb; 129Xe; 132 Xe; 197Au; 208Pb; 209Bi; and 238U] with different dip angles in muscovite mica [7,30–33] has been used in the present work. In our experimental work [7], freshly cleaved thin sheet (250 lm) of natural muscovite mica was cut into a number of disks of 3 cm diameter each. The basal plane [0 0 1] of these
samples were irradiated with different heavy ions [58Ni(11.56 MeV/n); 93Nb (18.00 MeV/n); 197Au (15.69, 13.42, 11.40 MeV/n); 208 Pb(13.80 MeV/n); 238U(15.36, 10.00, 5.90 MeV/n)] (with fluence of 104 ions/cm2) with different dip angles (30o, 45o, 60o, and 75o) from UNILAC (Universal Linear Accelerator) heavy ion accelerator, GSI, Darmstadt, Germany. The irradiated samples were then etched in 40% HF at room temperature (27 °C) to reveal the maximum etchable track length. All measurements have been taken with an optical microscope with an accuracy of 0.2 lm. Measuring the etched cone length and applying the corrections due to the bulk etching, the total etchable range for different ions have been measured [7]. The standard deviation in the range measurements is with in 2.5% (i.e. experimental uncertainty of ±1–±4 lm). Various procedures regarding the heavy ion stopping are available in the literature, but in many cases there is a lack of anisotropic effect of the crystalline materials on range and energy loss calculations. The actual range, energy loss and other related parameters involved during ion penetration are important to establish the validity of the various theoretical and semi-empirical procedures and various experimental setups. There is a need to study the reliability of these procedures for complex crystalline materials. Various famous and available range formulations [SRIM, LISE++:0-[Hub90], LISE++:1-[Zie85], LISE++:8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (Without LS correction)] [17,20] have been used in the present work for range calculation in muscovite mica. All the experimentally measured heavy ions ranges (our experimental work [7] and experimental data from other authors also [30–33]) used in the present investigation have been corrected using the etching threshold concept of Toulemonde et al., [1]. Percentage deviation between corrected experimental and computed range values have been calculated for comparative analysis. 4. Range and stoping power formulations In order to check the reliability of different range and stopping power formulations for the calculation of heavy ions ranges in layered crystalline materials (mica in present case), five different procedures [SRIM, LISE++:0-[Hub90], LISE++:1-[Zie85], LISE++: 8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (Without LS correction)] [17,20] have been choosen for the present purpose. 4.1. SRIM code SRIM (Stopping and Range of Ions in Matter) results from the work by J. P. Biersack on range algorithms [34] and the work edited by J. F. Ziegler on stopping theory [35–39]. It is a group of programs [17], which calculate the range and stopping of ions (up to 2 GeV/n) into matter using a quantum mechanical treatment of ion–atom collisions [40]. Electronic stopping powers are deduced from those for protons by means of an effective-charge fraction assumed to be independent of the target. The charge state of the ion within the target is described using the concept of effective charge [41], which includes a velocity dependent state and long-range screening due to the collective electron sea of the target [40]. Stopping powers for compounds are determined on the basis of an extensive study of experimental data for proton, helium and lithium projectiles [42]. 4.2. LISE code
Fig. 1. Schematic diagram of muscovite mica [7].
The program LISE [43,44] called after the spectrometer of the same name [45] has been developed to calculate the transmission and yields of fragments produced and collected in a fragment separator.
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M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625 Table 2 Experimental [7,30–33] and calculated [17,20] range values for a variety of heavy ions with different incident angle in muscovite mica. Ion
Energy
Angle of incidence
Experimental Range (lm)
SRIM-08.04
58
11.56(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 13.04(MeV/u) 11.10(MeV/u) 9.20(MeV/u) 7.10(MeV/u) 5.20(MeV/u) 2.80(MeV/u) 0.95(MeV/u) 0.50(MeV/u) 12.50(MeV/n) 12.50(MeV/n) 12.50(MeV/n) 15.69(MeV/n) 13.42(MeV/n) 11.40(MeV/n) 13.80(MeV/n) 17.12(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 15.36(MeV/n) 5.90(MeV/n) 10.00(MeV/n) 10.00(MeV/n) 10.00(MeV/n) 10.00(MeV/n)
45° 30° 45° 60° 75° 45° 45° 45° 45° 45° 45° 45° 45° 30° 45° 60° 45° 45° 45° 45° 45° 15° 30° 45° 60° 75° 45° 45° 30° 45° 60° 75°
80.50 135.40 141.50 146.00 149.60 98.00 85.00 71.00 58.00 45.00 31.00 18.00 5.00 96.40 103.50 112.00 108.90 90.00 79.20 95.60 125.40 89.00 92.50 95.60 99.70 103.10 107.80 41.70 62.60 69.40 74.50 78.00
93.93 154.18 154.18 154.18 154.18 96.31 81.16 67.20 52.70 40.27 25.08 12.56 8.76 94.21 94.21 94.21 128.78 109.72 93.49 113.56 142.37 106.31 106.31 106.31 106.31 106.31 120.33 52.42 80.43 80.43 80.43 80.43
Nia Nba 93 Nba 93 Nba 93 Nba 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 132 Xeb 132 Xeb 132 Xeb 197 Aua 197 Aua 197 Aua 208 Pba 208 Pbc 209 d Bi 209 d Bi 209 d Bi 209 d Bi 209 d Bi 238 a U 238 a U 238 a U 238 a U 238 a U 238 a U
93
a b c d e f
(17)f (14) (9) (6) (3) (2) (5) (5) (9) (11) (-19) (30) (75) (2) (9) (16) (18) (22) (18) (19) (14) (19) (15) (11) (7) (3) (12) (26) (28) (16) (8) (3)
LISE++:8.3.107– 0-[Hub90] 91.93 151.41 151.41 151.41 151.41 97.75 82.00 67.65 53.03 40.90 27.02 14.08 10.05 95.51 95.51 95.51 116.75 99.04 84.17 103.45 130.06 96.78 96.78 96.78 96.78 96.78 117.42 50.86 77.81 77.81 77.81 77.81
(14)f (12) (7) (4) (1) (0) (4) (5) (9) (9) (13) (22) (101) (1) (8) (15) (7) (10) (6) (8) (4) (9) (5) (1) (3) (6) (9) (22) (24) (12) (4) (0)
LISE++:8.3.107– 1-[Zie85] 92.56 156.44 156.44 156.44 156.44 104.62 87.92 72.37 56.12 42.29 25.86 13.32 9.50 102.33 102.33 102.33 126.53 107.63 91.15 112.34 140.61 105.21 105.21 105.21 105.21 105.21 128.06 53.65 84.85 84.85 84.85 84.85
(15)f (16) (11) (7) (5) (7) (3) (2) (3) (6) (17) (26) (90) (6) (1) (9) (16) (20) (15) (18) (12) (18) (14) (10) (6) (2) (19) (29) (36) (22) (14) (9)
LISE++:8.3.107–2ATIMA1.2 (LS Theory) 92.88 158.59 158.59 158.59 158.59 100.77 83.78 68.32 52.36 38.88 22.80 9.89 6.25 98.24 98.24 98.24 127.28 107.54 91.10 111.35 141.17 104.59 104.59 104.59 104.59 104.59 129.40 55.14 85.42 85.42 85.42 85.42
(15)f (17) (12) (9) (6) (3) (1) (4) (10) (14) (26) (45) (25) (2) (5) (12) (17) (19) (15) (16) (13) (18) (13) (9) (5) (1) (20) (32) (36) (23) (15) (10)
LISE++:8.3.107–3-ATIMA1.2 (Without LS correction) 92.71 155.44 155.41 155.41 155.41 100.22 83.71 68.32 52.36 38.88 22.80 9.89 6.25 97.84 97.84 97.84 125.13 106.78 91.97 110.36 137.83 103.96 103.96 103.96 103.96 103.96 127.34 55.14 85.42 85.42 85.42 85.42
(15)f (15) (10) (6) (4) (2) (2) (4) (10) (14) (26) (45) (25) (1) (5) (13) (15) (19) (16) (15) (10) (17) (12) (9) (4) (1) (18) (32) (36) (23) (15) (10)
Our experimental work (Standard deviation varies between ± 1 and ± 4 lm) [7]. [30]. Standard deviation ± 2.2 lm [31]. Standard deviation varies between ± 1.5 and ± 2.2 lm [32]. Standard deviation varies between ± 2 and ± 4 lm [33]. h i R RExperimental % deviation i.e. Calculated 100. RExperimental
LISE++ is the new generation of the LISE code, which allows the creation of a spectrometer with different sections. The LISE++ package [20,46] consists of utilities developed within the framework of the LISE++ program and existing programs ported from FORTRAN to C++. New utilities were developed and incorporated in LISE++ in addition to the already existing tools such as the physical parameters calculator, database of nuclear properties and relativistic two-body kinematics calculations. Four methods are available in the LISE code for energy loss calculation. The abbreviation is like in the code
4.3. Tables of Hubert et al., 1990 These tables [47] are an update to an earlier procedure of Hubert et al. [49] for calculating the stopping powers of various solids for different heavy ions. Stopping powers and ranges are tabulated for ions ð2 6 Z 1 6 103Þ in the energy region (2.5–500 MeV/n) for various solid materials. These calculations use stopping powers for a-particles and a new parameterization for the heavy-ion effective charge deduced from a set of about 600 experimental data points. 4.4. ATIMA code
i. 0-[Hub90] (Helium-based parameterization of Hubert et al., [47], the starting point at 2.5 AMeV is given by the range tables of Northcliffe and Schilling [48]) ii. 1-[Zie85] (Hydrogen-based parameterization of Ziegler et al. [40]) iii. 2-ATIMA1.2 (Method based on the ATIMA program [15]) iv. 3-ATIMA1.2 without LS-correction (Method based on the ATIMA program [15]). The ‘‘ATIMA1.2 without LS-correction” method was incorporated in the procedure to show the influence of the LS-correction. The energy loss is calculated for atomic numbers ð1 6 Z 1 6 130Þ and energies from 10 KeV in materials from hydrogen up to uranium. The calculation of energy loss in gas and composite materials is also included in the program.
ATIMA (ATomic Interaction with Matter) is a program [15] developed at GSI which calculates various physical quantities (Stopping Power, Energy Loss, Energy-loss Straggling, Angular Straggling, Range, Range Straggling and other beam parameters like Magnetic rigidity, time of flight, velocity etc.) characterizing the slowing down of protons and heavy ions in matter for specific kinetic energies ranging from 1 KeV/n to 500 GeV/n. Above 30 MeV/n, the stopping power is obtained from the theory by Lindhard and Sorensen [50], which includes the following corrections: i. The Shell corrections (Barkas and Berger) [51] ii. Barkas term (Jackson and McCarthy; Lindhard) [52,53] iii. The Fermi-density effect (Sternheimer and Peierls) [54]
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Table 3 Percentage deviationf between experimental(corrected) (Toulemonde et al. [1]) and calculated [17,20] range values for different heavy ions incident at different angle in muscovite mica. Ion
Energy
Angle of incidence
Experimental Range (Corrected) (lm)
SRIM08.04
LISE++:8.3.107– 0-[Hub90]
LISE++:8.3.107– 1-[Zie85]
LISE++:8.3.107–2ATIMA1.2 (LS Theory)
LISE++:8.3.107–3-ATIMA1.2 (Without LS correction)
58
11.56(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 13.04(MeV/u) 11.10(MeV/u) 9.20(MeV/u) 7.10(MeV/u) 5.20(MeV/u) 2.80(MeV/u) 0.95(MeV/u) 0.50(MeV/u) 12.50(MeV/n) 12.50(MeV/n) 12.50(MeV/n) 15.69(MeV/n) 13.42(MeV/n) 11.40(MeV/n) 13.80(MeV/n) 17.12(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 15.36(MeV/n) 5.90(MeV/n) 10.00(MeV/n) 10.00(MeV/n) 10.00(MeV/n) 10.00(MeV/n)
45° 30° 45° 60° 75° 45° 45° 45° 45° 45° 45° 45° 45° 30° 45° 60° 45° 45° 45° 45° 45° 15° 30° 45° 60° 75° 45° 45° 30° 45° 60° 75°
84.85 138.48 144.58 149.08 152.68 100.33 87.33 73.33 60.33 47.33 33.33 20.33 7.33 98.73 105.83 114.33 111.34 92.44 81.64 96.70 126.50 90.06 93.56 96.66 100.76 104.16 108.80 42.70 63.60 70.40 75.50 79.00
11 11 7 3 1 4 7 8 13 15 25 38 20 5 11 18 16 19 15 17 13 18 14 10 6 2 11 23 26 14 7 2
8 9 5 2 1 3 6 8 12 14 19 31 37 3 10 16 5 7 3 7 3 7 3 0 4 7 8 19 22 11 3 2
9 13 8 5 2 4 0 1 7 11 22 34 30 4 3 11 14 16 12 16 11 17 12 9 4 1 18 26 33 21 12 7
9 15 10 6 4 0 4 7 13 18 32 51 15 0 7 14 14 16 12 15 12 16 12 8 4 0 19 29 34 21 13 8
9 12 7 4 2 0 4 7 13 18 32 51 15 1 8 14 12 16 13 14 9 15 11 8 3 0 17 29 34 21 13 8
Nia Nba 93 Nba 93 Nba 93 Nba 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 132 Xeb 132 Xeb 132 Xeb 197 Aua 197 Aua 197 Aua 208 Pba 208 Pbc 209 d Bi 209 d Bi 209 d Bi 209 d Bi 209 d Bi 238 a U 238 a U 238 a U 238 a U 238 a U 238 a U 93
a b c d e f
Our experimental work [7]. [30]. [31]. [32]. [33]. RCalculated RExperimental
½
RExperimental
ðCorrectedÞ
100.
ðCorrectedÞ
The projectiles are treated as point-like particles of a mean charge according to pierce and Blann [55]. Below 10 MeV/n, an older version of Ziegler’s SRIM [40] is used. In the intermediate energy range, interpolation between these two formulations is used.
5. Results and discussion The experimental data of heavy ions [viz: 58Ni; 93Nb; 129Xe; Xe; 197Au; 208Pb; 209Bi; and 238U] ranges with different dip angles and energies in muscovite mica and the values calculated using different famous formulations [SRIM, LISE++:0-[Hub90], LISE++:1[Zie85], LISE++:8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (Without LS correction)] [17,20] are presented in table 2. The percentage deviation between experimental and calculated range values has been calculated and given in the table. Table 2 shows that, the calculated values deviate significantly from the experimental range data in many cases. Then all these experimentally measured heavy ion ranges have been corrected using the etching threshold concept of Toulemonde et al., [1]. The range correction factor contributes significantly in experimentally measured range values. The enhanced experimental range values after the etching threshold correction and the deviations shown by all the adopted formulations are presented in Table 3. The etching threshold (dE/dX(Elec.) = 3.4 keV/nm) range corrections in case of mica for different heavy ions were calculated using 132
the semi-empirical formulation (SRIM-08.04) [17]. Table 4 presents the various parameters (Energy, dE/dX(Nucl.), range correction factor) at etching threshold point (dE/dX(Elec.) = 3.4 keV/nm) for different heavy ions in muscovite mica. These results are also presented in Fig. 2 for clarity. The range correction factor at etching threshold is minimum (1 lm) for 238U projectile at 6.00 MeV energy and maximum (4.35 lm) for 58Ni projectile at 7.92 MeV energy. The energy where the etching threshold (dE/dX(Elec.) = 3.4 keV/nm) reached is different for each ions. In case of 197Au ion, the etching threshold reached at 12.09 MeV, while its value is very low for other chosen projectiles. The value of dE/dX(Nucl.) (at dE/ dX(Elec.) = 3.4 keV/nm) is minimum (0.13 keV/nm) for 58Ni projectile and maximum (2.68 keV/nm) for 238U projectile.
Table 4 Various parameters at etching threshold [dE/dX(Elec.) = (3.4 keV/nm)] (using SRIM 08.04 [17]) for different heavy ions in muscovite mica. Ion
Energy (MeV)
dE/dX(Nucl.) (keV/nm)
Range correction factor (lm)
Ni Nb Xe Au Pb Bi U
7.92 8.27 8.02 12.09 6.01 5.86 6.00
0.13 0.35 0.72 1.32 2.13 2.20 2.68
4.35 3.08 2.33 2.44 1.10 1.06 1.00
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5
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
16
3 2
14
1
12
0 3
10
% Deviation
dE/dX (Nucl.)
RCF (µm)
4
2 1
6 4
0
2
-1
0 -2
12
E(MeV)
8
30
40
50
60
70
80
Dip Angle (Deg)
10
Fig. 3b. The range deficit [%] between experimental(corrected) [7] and calculated [17,20] ranges of 93Nb (18.00 MeV/n) ion in muscovite mica as a function of dip angle.
8 6 Ni
Nb
Xe
Au
Pb
Bi
U
Ions Fig. 2. Various parameters at etching threshold [dE/dX(Elec.) = 3.4 keV/nm] for different ions in muscovite mica.
For 58Ni (11.56 MeV/n) ion, it is clear from Table 3 that, the range values calculated using LISE++:0-[Hub90] formulation show minimum deviation (8%) from the corrected experimental values [7] as compared to the other adopted formulations (SRIM shows maximum deviation of 11%). Fig. 3a presents the dip angle (30°–75°) behaviour of the experimental [7] and calculated [17,20] range values of 93Nb (18.00 MeV/n) ion in muscovite mica. Fig. 3b shows the dip angle
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
160
100
158 156 154
80
152
Range (µm)
Range (µm)
150 148 146 144
60
40
142
20
140 138
0
136 134 30
40
50
60
70
80
Dip Angle (Deg) Fig. 3a. Dip angle dependence of experimental [7] and the calculated [17,20] range values of 93Nb (18.00 MeV/n) ions in muscovite mica.
0
2
4
6
8
10
12
14
Energy (MeV/u) Fig. 4a. Energy behaviour of experimental [33] and calculated [17,20] range values of 129Xe ions incident at 45° in muscovite mica.
M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
40
% Deviation
114 112 110 108 106 104 102 100 98 96 94 92 90 30
35
40
45
50
55
60
Dip Angle (Deg) Fig. 5a. Variation of experimental [30] and calculated [17,20] range values of 132Xe (12.50 MeV/n) ions with incident angle in muscovite mica.
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
6 4 2 0 -2 -4 -6 -8 -10 -12 -14
30
-16
20
-18 -20
10
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
116
Range (µm)
behaviour of the percentage deviations of the calculated 93Nb ion range values from the corrected experimental data. It is clear from these observations that the experimental and calculated range values for 93Nb (18.00 MeV/n) ion show overall good agreement (1%) at high dip angle (75°) and show maximum deviation at low dip angles. Among various adopted procedures for range calculation, the LISE++:0-[Hub90] code shows good results as compared to other formulations. Fig. 4a shows the energy (0.50–13.04 MeV/u) behaviour of the experimental [33] and the calculated [17,20] range values of 129 Xe ion in muscovite mica at incident angle of 45°. Fig. 4b shows the energy behaviour of the percentage deviations of the calculated 129 Xe ion range values from the corrected experimental range data. In this case, it is clear that the percentage deviation between the calculated and experimetal range values decreases as the incident energy of the 129Xe ion increases. At high energy (13.04 MeV/u), there is a good agreement [about 0% deviation for LISE++:8.3.107–3-ATIMA1.2 (Without LS correction) formulation] between calculated and experimental range values. At low energy (0.5 MeV/u and 0.15 MeV/u), there is large deviation (about 51%) between the caculated and experimental range values. The dip angle (30°–60°) dependance of the experimental [30] and calculated [17,20] range values of 132Xe (12.50 MeV/n) ions in muscovite mica detector is presented in Fig. 5a. Fig. 5b shows the dip angle behaviour of the percentage deviations of the calculated 132Xe ion range values from the corrected experimental range data. These results make clear that, for 132Xe (12.50 MeV/n) ion, the calculated range values at low dip angle show overall good agreement [1% for LISE++:8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (Without LS correction) formulations] with the experimental data as compared to high dip angle range values (18% for SRIM). Among all the adopted formulations of range calculation, the LISE++:1-[Zie85] code shows good results for all these dip angles (30°–60°) as compared to other choosen procedures. For 179Au ion, it is clear from Figs. 6a,b that the LISE++:0[Hub90] formulation presents overall good agreement between the calculated and exprimentally measured range values as
% Deviation
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30
35
40
45
50
55
60
Dip Angle (Deg)
0
Fig. 5b. The range deficit [%] between experimental(corrected) [30] and calculated [17,20] ranges of 132Xe (12.50 MeV/n) ions in muscovite mica as a function of dip angle.
-10 -20 -30 -40 -50 -60
0
2
4
6
8
10
12
14
Energy (MeV/u) Fig. 4b. The range deficit [%] between experimental(corrected) [33] and calculated [17,20] ranges of 129Xe ions in muscovite mica as a function of specific energy [MeV/u].
compared to the other adopted formulations in the given energy region (11.40–15.69 MeV/n). For 208Pb projectile ranges [7,31] in muscovite mica at dip angle of 45° (from Table 3), the LISE++:0-[Hub90] formulation tabulates good range values and show minimum range deficit as compared to other codes. The range deficit is minimum for high energy (17.12 MeV/n) as compared to low energy (13.80 MeV/n) 208Pb ion. The variation of the experimental [30] and calculated [17,20] range values for 209Bi (13.01 MeV/n) ions in muscovite mica detector with dip angle (15°–75°) is presented in Fig. 7a. Fig. 7b shows
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M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction) 108
125
106
120
104
115
102
110
100
Range (µm)
Range (µm)
130
105 100 95
98 96 94
90
92 85
90 80
88 75 11
12
13
14
15
16
10
20
30
Energy (MeV/n)
50
60
70
80
Fig. 7a. Dip angle behaviour of experimental [32] and calculated [17,20] range values of 209Bi (13.01 MeV/n) heavy ions in muscovite mica.
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
20 18 16 14 12 10
% Deviation
% Deviation
Fig. 6a. Energy behaviour of experimental [7] and calculated [17,20] range values of 179Au heavy ions incident at 45° angle in muscovite mica.
21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3
40
Dip Angle (Deg)
8 6 4 2 0 -2 -4 -6 -8
11
12
13
14
15
16
Energy (MeV/n) Fig. 6b. The range deficit [%] between experimental(corrected) [7] and calculated [17,20] ranges of 179Au ions in muscovite mica as a function of specific energy [MeV/n].
the dip angle behaviour of percentage deviations of the calculated 209 Bi ion range values from the experimental measured range data. It is clear from these observations that the deficit between the calculated and experimental range values decreases [0% in case of LISE++:8.3.107–2-ATIMA1.2 (LS Theory)] towards higher dip angle [75°] as compared to low dip angle [18% for SRIM at 15°]. Among
10
20
30
40
50
60
70
80
Dip Angle (Deg) Fig. 7b. The range deficit [%] between experimental(corrected) [32] and calculated [17,20] ranges of 209Bi (13.01 MeV/n) ions in muscovite mica as a function of dip angle.
all the adopted procedures of range calculation, the LISE++:0[Hub90] formulation shows overall good results at all dip angles (15°–75°) as compared to other choosen codes. Fig. 8a presents the dip angle (30°–75°) dependance of the experimental [7] and calculated [17,20] range values of 238U (10.00 MeV/n) ion in muscovite mica. Fig. 8b shows the dip angle
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M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
88
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
140 130
86 84
120
82
110
80
100
Range (µm)
Range (µm)
78 76 74 72
90 80 70
70
60
68 66
50
64
40
62
6 30
40
50
60
70
8
80
10
12
14
16
Energy (MeV/n)
Dip Angle (Deg) Fig. 8a. Dip angle behaviour of experimental [7] and calculated [17,20] range values of 238U (10.00 MeV/n) heavy ions in muscovite mica.
Fig. 9a. Energy behaviour of experimental [7] and calculated [17,20] range values of 238U heavy ions incident at 45° angle in muscovite mica.
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
30 28 26
35
24 30
% Deviation
22
% Deviation
25 20 15
20 18 16 14
10
12 10
5
8 0
6
8
10
12
14
16
Energy (MeV/n)
-5 30
40
50
60
70
80
Dip Angle (Deg)
Fig. 9b. The range deficit [%] between experimental(corrected) [7] and calculated [17,20] ranges of 238U ions in muscovite mica as a function of specific energy [MeV/n].
Fig. 8b. The range deficit [%] between experimental(corrected) [7] and calculated [17,20] ranges of 238U (10.00 MeV/n) ion in muscovite mica as a function of dip angle.
behaviour of percentage deviations of the calculated 238U ion range values from the experimentally measured range data. For 238U (10.00 MeV/n) ion projectile, the percentage deviation between the calculated and experimental range values decreases as the angle of incidence increases. LISE++:0-[Hub90] tabulated range values show overall good agreement for all choosen dip angles
(30°–75°) as compared to the rest of the formulations. It is also clear from Figs. 9a,b that the percentage deviation between the calculated and experimental range values decreases as the incident energy of the 238U ion (dip angle of 45°) increases. At high energy, there is a good agreement between LISE++:0-[Hub90] formulation tabulated and experimental range values. At low energy, there is large deviation between the caculated and experimental range values.
M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
From all these observations, it is interesting to note that the heavy ion range values calculated using all the adopted formulations deviate significantly from the experimentally measured data in muscovite mica. This might be due to the reasons that the procedures involved in most of the present theoretical and semiempirical stopping formulations are not dip angle dependent. The dip angle dependent stopping processes might be due to inhomogeneity of various properties of the detectors in different orientations. The penetrating projectile observes different interaction processes in different orientation of the materials, thus it covers different path in different directions. 6. Conclusion The experimental observations lead to the conclusion that most of the available procedures for range and energy loss calculation of ions do not account the anisotropic effect on stopping processes in layered crystalline materials like mica. The dip angle dependent stopping parameters can play significant role in ion stopping ideas in this type of complex structures. These types of crystalline materials are made up of three-dimensional array of atoms arranged in an orderly fashion, and the ion movement is very much directional dependent. The physical (absorbance, refractive index, magnetic field, density, etc.), mechanical (frictional forces, elastic moduli etc.) and chemical properties (different atomic and bonding environs) often differ with orientation in these types of materials and in relation to these properties, atoms are able to distort one another easier in some directions than others. The dip angle dependent stopping processes might be due to inhomogeneity of these properties of the detectors in different orientations. The ionic field of the penetrating projectile exerts different action (interaction processes) in different orientation of the crystalline materials, thus the anisotropic ion energy loss consumes different intensity. When the stopping medium is anisotropic or inhomogeneous, the finite geometrical dimensions of the material cannot be ignored or minimised and the detailed geometric modeling of ion propagation through these types of diverse materials (like mica) is required. It is strongly recommended that the stopping parameters affected by the anisotropic structure of the detecting materials should be studied and analysed for better calculations of various heavy ion stopping processes in crystalline media. Acknowledgments One of the authors (M. Singh) is thankful to the Council of Scientific and Industrial Research (CSIR, India) for Research Associateship. References [1] [2] [3] [4] [5] [6] [7] [8]
M. Toulemonde, S. Bouffard, F. Studer, Nucl. Instrum. Meth. B 91 (1994) 108. S.A. Durrani, Radiat. Meas. 34 (2001) 5. Editorial, Nucl. Instrum. Meth. B 195 (2002) 1. D. Fink, P.S. Alegaonkar, A.V. Petrov, A.S. Berdinsky, V. Rao, M. Muller, K.K. Dwivedi, L.T. Chadderton, Radiat. Meas. 36 (2003) 605. D. Fink, L.T. Chadderton, Radiat. Eff. Def. Sol. 160 (2005) 67. ICRU-73, Stopping of ions heavier than helium, Journal of the ICRU 5, Oxford University Press, 2005. L. Singh, M. Singh, K.S. Samra, R. Singh, Nucl. Instrum. Meth. B 248 (2006) 117. P. Sigmund, Particle Penetration and Radiation Effects, Springer Series in SolidState Sciences, vol. 151, Springer, Berlin, 2006.
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[9] L. Singh, M. Singh, K.S. Samra, R. Singh, Radiat. Eff. Def. Sol. 162 (2007) 333. [10] D. Fink, A. Chandra, W.R. Fahrner, K. Hoppe, H. Winkelmann, A. Saad, P. Alegaonkar, A. Berdinsky, D. Grasser, R. Lorenz, Vac 82 (2008) 900. [11] J.F. Ziegler, J.P. Biersack, M.D. Ziegler, SRIM: The Stopping and Range of Ions in Matter, SRIM Co., Chester, MD, USA, 2008. [12] P.B. Price, Radiat. Meas. 43 (2008) S13. [13] S. Agostinelli, J. Allison, K. Amako, et al., Nucl. Instr. Meth. A 506 (2003) 250. [14] M. Singh, L. Singh, Radiat. Eff. Def. Sol. 163 (2008) 605. [15] H. Geissel, C. Scheidenberger, P. Malzacher, ATIMA (ATomic Interaction with MAtter), Available on http://www-linux.gsi.de/~weick/atima, 2009. [16] H. Paul, Stopping Power for Light Ions, MSTAR version 3.12, Available on www.exphys.unilinz.ac.at/stopping, 2009. [17] J.F. Ziegler, SRIM–2008, the Stopping and Range of Ions in Matter, Available on www.srim.org, 2009. [18] L. Singh, M. Singh, N. Kaur, B. Singh, Indian J. Phys. 83 (2009) 1109. [19] M. Singh, B. Singh, N. Kaur, L. Singh, Indian J. Phys. 83 (2009) 1099. [20] O.B. Tarasov, D. Bazin, The LISE code, Available on http://dnr080.jinr.ru/lise and http://www.nscl.msu.edu/lise, 2009. [21] P.L. Grande, G. Schiwietz, CasP4.0, Available on www.hmi.de/people/ schiwietz/casp.html, 2009. [22] M. Lang, U.A. Glasmacher, B. Moine, R. Neumann, G.A. Wagner, Nucl. Instr. Meth. B 218 (2004) 466. [23] S.R. Hashemi-Nezhad, Nucl. Instr. Meth. B 234 (2005) 533. [24] M. Singh, L. Singh, B. Singh, Indian J. Phys. 83 (2009) 977. [25] M. Singh, N. Kaur, L. Singh, Radiat. Phys. Chem. (2010) (Communicated). [26] L. Singh, J. Singh, S. Singh, H.S. Virk, Nucl. Geophys. 5 (1991) 361. [27] Y. Kuwahara, The cleaved surface structure of muscovite by fluid contact mode AFM (in Japanese), Hikaku Shakai Bunka, Bull Graduate School of Social and Cultural Studies, Kyushu University 4 (1998) 137. [28] Y. Kuwahara, Phys. Chem. Min. 26 (1999) 198. [29] M. Rieder, G. Cavazzini, Y.S. D’Yakonov, V.A. Frank-Kamenetskii, G. Gottardi, et al., Can. Mineral. 36 (1998) 905. [30] L.T. Chadderton, S. Ghosh, A. Saxena, K.K. Dwivedi, J.P. Biersack, W. Fink, Nucl. Instr. Meth. B 46 (1990) 46. [31] S. Ghosh, J. Raju, K.K. Dwivedi, Radiat. Meas. 24 (1995) 171. [32] S. Ghosh, K.K. Dwivedi, Radiat. Meas. 28 (1997) 33. [33] A. Kulshreshtha, C. Laldawngliana, R. Mishra, S. Ghosh, K.K. Dwivedi, R. Brandt, D. Fink, Radiat. Eff. Def. Sol. 147 (1999) 151. [34] J.P. Biersack, L.G. Haggmark, Nucl. Instr. Meth. 174 (1980) 257. [35] H.H. Andersen, Bibliography and Index of Experimental Range and Stopping Power Data, vol. 2, Stopping and Ranges of Ions in Matter, Pergamon Press, New York, 1977. [36] H.H. Andersen, J.F. Ziegler, Hydrogen Stopping Powers and Ranges in All Elements, vol. 3 ‘‘Stopping and Ranges of Ions in Matter”, Pergamon Press, New York, 1977. [37] J.F. Ziegler, Helium Stopping Powers and Ranges in All Elements, vol. 4 ‘‘The Stopping and Ranges of Ions in Matter”, Pergamon Press, New York, 1977. [38] J.F. Ziegler, Handbook of Stopping Cross-sections for Energetic Ions in All Elements, vol. 5 ‘‘The Stopping and Ranges of Ions in Matter”, Pergamon Press, New York, 1980. [39] U. Littmark, J.F. Ziegler, Handbook of Range Distributions for Energetic Ions in All Elements, Vol. 6, ‘‘The Stopping and Ranges of Ions in Matter”, Pergamon Press, New York, 1980. [40] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids. Vol. 1, ‘‘The Stopping and Ranges of Ions in Matter”, Pergamon Press, New York, 1985. [41] W. Brandt, M. Kitagawa, Phys. Rev. B 25 (1982) 5631. [42] J.F. Ziegler, J.M. Manoyan, Nucl. Instr. Meth. B 35 (1988) 215. [43] D. Bazin, O. Tarasov, M. Lewitowicz, O. Sorlin, Nucl. Instr. Meth. A 482 (2002) 307. [44] O. Tarasov, D. Bazin, M. Lewitowicz, O. Sorlin, Nucl. Phys. A 701 (2002) 661. [45] R. Anne, D. Bazin, A.C. Mueller, J.C. Jacmart, M. Langevin, Nucl. Instr. Meth. A 257 (1987) 215. [46] O.B. Tarasov, D. Bazin, Nucl. Phys. A 746 (2004) 411. [47] F. Hubert, R. Bimbot, H. Gauvin, At. Data Nucl. Data Tables 46 (1990) 1. [48] L.C. Northcliffe, R.F. Schilling, At. Data. Nucl. Data Tables 7 (1970) 233. [49] F. Hubert, R. Bimbot, H. Gauvin, Nucl. Instr. Meth. B 36 (1989) 357. [50] J. Lindhard, A.H. Sorensen, Phys. Rev. A 53 (1996) 2443. [51] W.H. Barkas, M.J. Berger, Heavy Charged Particle Energy Losses and RangesTables, NASA-SP-3013, 1964. [52] J.D. Jackson, R.L. McCarthy, Phys. Rev. B 6 (1972) 4131. [53] J. Lindhard, Nucl. Instr. Meth. 132 (1976) 1. [54] R.M. Sternheimer, R.F. Peierls, Phys. Rev. B 3 (1971) 3681. [55] T.E. Pierce, M. Blann, Phys, Rev. 173 (1968) 390.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Heavy ion range anisotropy in muscovite mica Mohan Singh, Navjeet Kaur, Lakhwant Singh * Department of Physics, Guru Nanak Dev University, Amritsar, Punjab-143005, India
a r t i c l e
i n f o
Article history: Received 26 November 2009 Received in revised form 11 June 2010 Available online 1 July 2010 Keywords: Muscovite mica Layered crystal Heavy ions Stopping processes Anisotropy
a b s t r a c t The anisotropy of heavy ion range in layered crystal of muscovite mica has been studied in the present investigation. The freshly cleaved basal plane of the natural muscovite mica has been irradiated with various energetic heavy ions with different dip angles from UNILAC (Universal Linear Accelerator) heavy ion accelerator, GSI, Darmstadt, Germany. We have tried to investigate the causes and effects of the anisotropic nature of the layered crystalline mica on heavy ions propagation. The measured and available range values of number of heavy ions [viz: 58Ni; 93Nb; 129Xe; 132Xe; 197Au; 208Pb; 209Bi; and 238U] in muscovite mica are used to highlight the shortcomings of various range and energy loss formulations about the orientation effect on stopping processes in anisotropic media. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Because of the great importance and interest, the field of ion matter interaction explores many unique and diverse applications in various fields of science and technology. These interests and applications require a complete experimental and theoretical study of the irradiated materials for deep understanding of the different processes involved during the ions propagation [1–12]. The progress in accelerator technology and availability of a variety of beams of varying energy, masses and charge, availability of special type of radiation detectors, advanced instruments and development of new computational methods have led to several new demands in this field of science. In order to understand the mechanism of ion stopping, enormous work has been done on both theoretical and experimental sides. However, despite extensive research over almost a century, several central problems (incomplete knowledge of stopping processes) remain unsolved. It is important to find the solution of these problems and develop new ideas in experiments and theories. The interest for the complete knowledge about the basic fundamental processes responsible for the slowing down of energetic heavy ions in anisotropic material remains alive. Because of the complexities involved in the structures of these types of layered crystalline materials, various processes during ion penetration behave completely different from their amorphous counterparts. The layered crystalline structure has a large effect on the range and stopping of projectiles [7]. Various theoretical and semi-empirical formulations are present to study the ion stopping processes
* Corresponding author. Tel.: +91 183 2450926; fax: +91 183 2258820. E-mail address: [email protected] (L. Singh). 0168-583X/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2010.06.024
[6,13–21], but there is no satisfactory treatment to provide a quantitative understanding of the phenomena involved in anisotropic media. Among various radiation detecting materials, the minerals (e.g., Mica) provide unique opportunity to measure the radiation effects and defects because of the better measurement of damage [7,22– 26]. The irradiated mica can provide enormous important applications in science and technology. Due to this, there is a dire need of studying various heavy ion stopping processes in it. In the present work, the anisotropic nature of layered crystal of muscovite mica has been investigated by studying the dip angle dependence of heavy ions ranges. We have tried to investigate the causes and effects of the anisotropic nature of the muscovite mica on heavy ions ranges. Various famous and available range formulations [SRIM, LISE++:0-[Hub90], LISE++:1-[Zie85], LISE++:8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (without LS correction)] [17,20] have been used to check their reliability about the orientation effect on the heavy ions range calculations. 2. Muscovite mica Minerals consist of negatively charge silicate layers bonded together by interlayer cations. Mica belongs to a family of minerals known as phyllosilicates. It has a monoclinic structure with unit structure consisting of one octahedral sheet sandwiching between two opposing tetrahedral sheets. It crystallizes in a layered structure and can be cleaved relatively easily into thin translucent sheets. These sheets form a layer that is separated from adjacent layers by planes of non-hydrated interlayer cations. In the present investigation, natural muscovite mica (q = 2.80 gm/cm3; crystallographic system: monoclinic [22,27–29]) was
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Table 1 Electron-microprobe data for muscovite mica. Oxide
Weight%
Element
Weight%
Na2O MgO Al2O3 SiO2 K2O TiO2 FeO MnO Total H2O(assumed)
0.68 0.16 35.17 47.00 10.49 0.02 2.29 0.03 95.84 4.16
Na Mg Al Si K Ti Fe Mn O Total
0.51 0.10 18.61 21.96 8.70 0.01 1.78 0.03 44.13 95.84
collected from Nilore Mica belt, India. The chemical compositional analysis of the ‘‘as received” sample was carried out using the Electron Probe Microanalyser at IIT Roorkee, India. The results of the microprobe analysis are listed in Table 1. The structural formula of the muscovite mica calculated on the basis of EPMA is (K0.87 Na0.08)R0.95(Al1.98Mg0.02)R2.00 (Al0:72 Fe3þ 0:25 Si3:06 )R4.03O10(OH)1.81. Muscovite mica has layered structure consisting of series of sheets stacked parallel to each other [7]. It consists of infinite sheets of corner-shared SiO4 tetrahedra, with the apical oxygen atoms located at the corners of a hexagon. In this structure, onefourth of the Si is replaced by Al, with the remaining K+ and Al3+ ions lying in between the aluminosilicate sheets. A single octahedral AlO6 sheet is sandwiched between two tetrahedral SiO4 sheets, with a layer of K+ ions located between the trilayer aluminosilicate sheets (Fig. 1). Since the ionic bonding between the K+ layers and the trilayer aluminosilicate sheet is weak, mica cleaves rather easily at the positions of the K+ layers. The most stable surface [0 0 1] was used for heavy ion irradiation after cleaving the muscovite crystal [7,24].
3. Methodology In order to understand the orientation effect of layered crystalline materials on heavy ion stopping processes, the experimental range data for a variety of heavy ions [viz: 58Ni; 93Nb; 129Xe; 132 Xe; 197Au; 208Pb; 209Bi; and 238U] with different dip angles in muscovite mica [7,30–33] has been used in the present work. In our experimental work [7], freshly cleaved thin sheet (250 lm) of natural muscovite mica was cut into a number of disks of 3 cm diameter each. The basal plane [0 0 1] of these
samples were irradiated with different heavy ions [58Ni(11.56 MeV/n); 93Nb (18.00 MeV/n); 197Au (15.69, 13.42, 11.40 MeV/n); 208 Pb(13.80 MeV/n); 238U(15.36, 10.00, 5.90 MeV/n)] (with fluence of 104 ions/cm2) with different dip angles (30o, 45o, 60o, and 75o) from UNILAC (Universal Linear Accelerator) heavy ion accelerator, GSI, Darmstadt, Germany. The irradiated samples were then etched in 40% HF at room temperature (27 °C) to reveal the maximum etchable track length. All measurements have been taken with an optical microscope with an accuracy of 0.2 lm. Measuring the etched cone length and applying the corrections due to the bulk etching, the total etchable range for different ions have been measured [7]. The standard deviation in the range measurements is with in 2.5% (i.e. experimental uncertainty of ±1–±4 lm). Various procedures regarding the heavy ion stopping are available in the literature, but in many cases there is a lack of anisotropic effect of the crystalline materials on range and energy loss calculations. The actual range, energy loss and other related parameters involved during ion penetration are important to establish the validity of the various theoretical and semi-empirical procedures and various experimental setups. There is a need to study the reliability of these procedures for complex crystalline materials. Various famous and available range formulations [SRIM, LISE++:0-[Hub90], LISE++:1-[Zie85], LISE++:8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (Without LS correction)] [17,20] have been used in the present work for range calculation in muscovite mica. All the experimentally measured heavy ions ranges (our experimental work [7] and experimental data from other authors also [30–33]) used in the present investigation have been corrected using the etching threshold concept of Toulemonde et al., [1]. Percentage deviation between corrected experimental and computed range values have been calculated for comparative analysis. 4. Range and stoping power formulations In order to check the reliability of different range and stopping power formulations for the calculation of heavy ions ranges in layered crystalline materials (mica in present case), five different procedures [SRIM, LISE++:0-[Hub90], LISE++:1-[Zie85], LISE++: 8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (Without LS correction)] [17,20] have been choosen for the present purpose. 4.1. SRIM code SRIM (Stopping and Range of Ions in Matter) results from the work by J. P. Biersack on range algorithms [34] and the work edited by J. F. Ziegler on stopping theory [35–39]. It is a group of programs [17], which calculate the range and stopping of ions (up to 2 GeV/n) into matter using a quantum mechanical treatment of ion–atom collisions [40]. Electronic stopping powers are deduced from those for protons by means of an effective-charge fraction assumed to be independent of the target. The charge state of the ion within the target is described using the concept of effective charge [41], which includes a velocity dependent state and long-range screening due to the collective electron sea of the target [40]. Stopping powers for compounds are determined on the basis of an extensive study of experimental data for proton, helium and lithium projectiles [42]. 4.2. LISE code
Fig. 1. Schematic diagram of muscovite mica [7].
The program LISE [43,44] called after the spectrometer of the same name [45] has been developed to calculate the transmission and yields of fragments produced and collected in a fragment separator.
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M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625 Table 2 Experimental [7,30–33] and calculated [17,20] range values for a variety of heavy ions with different incident angle in muscovite mica. Ion
Energy
Angle of incidence
Experimental Range (lm)
SRIM-08.04
58
11.56(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 13.04(MeV/u) 11.10(MeV/u) 9.20(MeV/u) 7.10(MeV/u) 5.20(MeV/u) 2.80(MeV/u) 0.95(MeV/u) 0.50(MeV/u) 12.50(MeV/n) 12.50(MeV/n) 12.50(MeV/n) 15.69(MeV/n) 13.42(MeV/n) 11.40(MeV/n) 13.80(MeV/n) 17.12(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 15.36(MeV/n) 5.90(MeV/n) 10.00(MeV/n) 10.00(MeV/n) 10.00(MeV/n) 10.00(MeV/n)
45° 30° 45° 60° 75° 45° 45° 45° 45° 45° 45° 45° 45° 30° 45° 60° 45° 45° 45° 45° 45° 15° 30° 45° 60° 75° 45° 45° 30° 45° 60° 75°
80.50 135.40 141.50 146.00 149.60 98.00 85.00 71.00 58.00 45.00 31.00 18.00 5.00 96.40 103.50 112.00 108.90 90.00 79.20 95.60 125.40 89.00 92.50 95.60 99.70 103.10 107.80 41.70 62.60 69.40 74.50 78.00
93.93 154.18 154.18 154.18 154.18 96.31 81.16 67.20 52.70 40.27 25.08 12.56 8.76 94.21 94.21 94.21 128.78 109.72 93.49 113.56 142.37 106.31 106.31 106.31 106.31 106.31 120.33 52.42 80.43 80.43 80.43 80.43
Nia Nba 93 Nba 93 Nba 93 Nba 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 132 Xeb 132 Xeb 132 Xeb 197 Aua 197 Aua 197 Aua 208 Pba 208 Pbc 209 d Bi 209 d Bi 209 d Bi 209 d Bi 209 d Bi 238 a U 238 a U 238 a U 238 a U 238 a U 238 a U
93
a b c d e f
(17)f (14) (9) (6) (3) (2) (5) (5) (9) (11) (-19) (30) (75) (2) (9) (16) (18) (22) (18) (19) (14) (19) (15) (11) (7) (3) (12) (26) (28) (16) (8) (3)
LISE++:8.3.107– 0-[Hub90] 91.93 151.41 151.41 151.41 151.41 97.75 82.00 67.65 53.03 40.90 27.02 14.08 10.05 95.51 95.51 95.51 116.75 99.04 84.17 103.45 130.06 96.78 96.78 96.78 96.78 96.78 117.42 50.86 77.81 77.81 77.81 77.81
(14)f (12) (7) (4) (1) (0) (4) (5) (9) (9) (13) (22) (101) (1) (8) (15) (7) (10) (6) (8) (4) (9) (5) (1) (3) (6) (9) (22) (24) (12) (4) (0)
LISE++:8.3.107– 1-[Zie85] 92.56 156.44 156.44 156.44 156.44 104.62 87.92 72.37 56.12 42.29 25.86 13.32 9.50 102.33 102.33 102.33 126.53 107.63 91.15 112.34 140.61 105.21 105.21 105.21 105.21 105.21 128.06 53.65 84.85 84.85 84.85 84.85
(15)f (16) (11) (7) (5) (7) (3) (2) (3) (6) (17) (26) (90) (6) (1) (9) (16) (20) (15) (18) (12) (18) (14) (10) (6) (2) (19) (29) (36) (22) (14) (9)
LISE++:8.3.107–2ATIMA1.2 (LS Theory) 92.88 158.59 158.59 158.59 158.59 100.77 83.78 68.32 52.36 38.88 22.80 9.89 6.25 98.24 98.24 98.24 127.28 107.54 91.10 111.35 141.17 104.59 104.59 104.59 104.59 104.59 129.40 55.14 85.42 85.42 85.42 85.42
(15)f (17) (12) (9) (6) (3) (1) (4) (10) (14) (26) (45) (25) (2) (5) (12) (17) (19) (15) (16) (13) (18) (13) (9) (5) (1) (20) (32) (36) (23) (15) (10)
LISE++:8.3.107–3-ATIMA1.2 (Without LS correction) 92.71 155.44 155.41 155.41 155.41 100.22 83.71 68.32 52.36 38.88 22.80 9.89 6.25 97.84 97.84 97.84 125.13 106.78 91.97 110.36 137.83 103.96 103.96 103.96 103.96 103.96 127.34 55.14 85.42 85.42 85.42 85.42
(15)f (15) (10) (6) (4) (2) (2) (4) (10) (14) (26) (45) (25) (1) (5) (13) (15) (19) (16) (15) (10) (17) (12) (9) (4) (1) (18) (32) (36) (23) (15) (10)
Our experimental work (Standard deviation varies between ± 1 and ± 4 lm) [7]. [30]. Standard deviation ± 2.2 lm [31]. Standard deviation varies between ± 1.5 and ± 2.2 lm [32]. Standard deviation varies between ± 2 and ± 4 lm [33]. h i R RExperimental % deviation i.e. Calculated 100. RExperimental
LISE++ is the new generation of the LISE code, which allows the creation of a spectrometer with different sections. The LISE++ package [20,46] consists of utilities developed within the framework of the LISE++ program and existing programs ported from FORTRAN to C++. New utilities were developed and incorporated in LISE++ in addition to the already existing tools such as the physical parameters calculator, database of nuclear properties and relativistic two-body kinematics calculations. Four methods are available in the LISE code for energy loss calculation. The abbreviation is like in the code
4.3. Tables of Hubert et al., 1990 These tables [47] are an update to an earlier procedure of Hubert et al. [49] for calculating the stopping powers of various solids for different heavy ions. Stopping powers and ranges are tabulated for ions ð2 6 Z 1 6 103Þ in the energy region (2.5–500 MeV/n) for various solid materials. These calculations use stopping powers for a-particles and a new parameterization for the heavy-ion effective charge deduced from a set of about 600 experimental data points. 4.4. ATIMA code
i. 0-[Hub90] (Helium-based parameterization of Hubert et al., [47], the starting point at 2.5 AMeV is given by the range tables of Northcliffe and Schilling [48]) ii. 1-[Zie85] (Hydrogen-based parameterization of Ziegler et al. [40]) iii. 2-ATIMA1.2 (Method based on the ATIMA program [15]) iv. 3-ATIMA1.2 without LS-correction (Method based on the ATIMA program [15]). The ‘‘ATIMA1.2 without LS-correction” method was incorporated in the procedure to show the influence of the LS-correction. The energy loss is calculated for atomic numbers ð1 6 Z 1 6 130Þ and energies from 10 KeV in materials from hydrogen up to uranium. The calculation of energy loss in gas and composite materials is also included in the program.
ATIMA (ATomic Interaction with Matter) is a program [15] developed at GSI which calculates various physical quantities (Stopping Power, Energy Loss, Energy-loss Straggling, Angular Straggling, Range, Range Straggling and other beam parameters like Magnetic rigidity, time of flight, velocity etc.) characterizing the slowing down of protons and heavy ions in matter for specific kinetic energies ranging from 1 KeV/n to 500 GeV/n. Above 30 MeV/n, the stopping power is obtained from the theory by Lindhard and Sorensen [50], which includes the following corrections: i. The Shell corrections (Barkas and Berger) [51] ii. Barkas term (Jackson and McCarthy; Lindhard) [52,53] iii. The Fermi-density effect (Sternheimer and Peierls) [54]
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Table 3 Percentage deviationf between experimental(corrected) (Toulemonde et al. [1]) and calculated [17,20] range values for different heavy ions incident at different angle in muscovite mica. Ion
Energy
Angle of incidence
Experimental Range (Corrected) (lm)
SRIM08.04
LISE++:8.3.107– 0-[Hub90]
LISE++:8.3.107– 1-[Zie85]
LISE++:8.3.107–2ATIMA1.2 (LS Theory)
LISE++:8.3.107–3-ATIMA1.2 (Without LS correction)
58
11.56(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 18.00(MeV/n) 13.04(MeV/u) 11.10(MeV/u) 9.20(MeV/u) 7.10(MeV/u) 5.20(MeV/u) 2.80(MeV/u) 0.95(MeV/u) 0.50(MeV/u) 12.50(MeV/n) 12.50(MeV/n) 12.50(MeV/n) 15.69(MeV/n) 13.42(MeV/n) 11.40(MeV/n) 13.80(MeV/n) 17.12(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 13.01(MeV/n) 15.36(MeV/n) 5.90(MeV/n) 10.00(MeV/n) 10.00(MeV/n) 10.00(MeV/n) 10.00(MeV/n)
45° 30° 45° 60° 75° 45° 45° 45° 45° 45° 45° 45° 45° 30° 45° 60° 45° 45° 45° 45° 45° 15° 30° 45° 60° 75° 45° 45° 30° 45° 60° 75°
84.85 138.48 144.58 149.08 152.68 100.33 87.33 73.33 60.33 47.33 33.33 20.33 7.33 98.73 105.83 114.33 111.34 92.44 81.64 96.70 126.50 90.06 93.56 96.66 100.76 104.16 108.80 42.70 63.60 70.40 75.50 79.00
11 11 7 3 1 4 7 8 13 15 25 38 20 5 11 18 16 19 15 17 13 18 14 10 6 2 11 23 26 14 7 2
8 9 5 2 1 3 6 8 12 14 19 31 37 3 10 16 5 7 3 7 3 7 3 0 4 7 8 19 22 11 3 2
9 13 8 5 2 4 0 1 7 11 22 34 30 4 3 11 14 16 12 16 11 17 12 9 4 1 18 26 33 21 12 7
9 15 10 6 4 0 4 7 13 18 32 51 15 0 7 14 14 16 12 15 12 16 12 8 4 0 19 29 34 21 13 8
9 12 7 4 2 0 4 7 13 18 32 51 15 1 8 14 12 16 13 14 9 15 11 8 3 0 17 29 34 21 13 8
Nia Nba 93 Nba 93 Nba 93 Nba 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 129 Xee 132 Xeb 132 Xeb 132 Xeb 197 Aua 197 Aua 197 Aua 208 Pba 208 Pbc 209 d Bi 209 d Bi 209 d Bi 209 d Bi 209 d Bi 238 a U 238 a U 238 a U 238 a U 238 a U 238 a U 93
a b c d e f
Our experimental work [7]. [30]. [31]. [32]. [33]. RCalculated RExperimental
½
RExperimental
ðCorrectedÞ
100.
ðCorrectedÞ
The projectiles are treated as point-like particles of a mean charge according to pierce and Blann [55]. Below 10 MeV/n, an older version of Ziegler’s SRIM [40] is used. In the intermediate energy range, interpolation between these two formulations is used.
5. Results and discussion The experimental data of heavy ions [viz: 58Ni; 93Nb; 129Xe; Xe; 197Au; 208Pb; 209Bi; and 238U] ranges with different dip angles and energies in muscovite mica and the values calculated using different famous formulations [SRIM, LISE++:0-[Hub90], LISE++:1[Zie85], LISE++:8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (Without LS correction)] [17,20] are presented in table 2. The percentage deviation between experimental and calculated range values has been calculated and given in the table. Table 2 shows that, the calculated values deviate significantly from the experimental range data in many cases. Then all these experimentally measured heavy ion ranges have been corrected using the etching threshold concept of Toulemonde et al., [1]. The range correction factor contributes significantly in experimentally measured range values. The enhanced experimental range values after the etching threshold correction and the deviations shown by all the adopted formulations are presented in Table 3. The etching threshold (dE/dX(Elec.) = 3.4 keV/nm) range corrections in case of mica for different heavy ions were calculated using 132
the semi-empirical formulation (SRIM-08.04) [17]. Table 4 presents the various parameters (Energy, dE/dX(Nucl.), range correction factor) at etching threshold point (dE/dX(Elec.) = 3.4 keV/nm) for different heavy ions in muscovite mica. These results are also presented in Fig. 2 for clarity. The range correction factor at etching threshold is minimum (1 lm) for 238U projectile at 6.00 MeV energy and maximum (4.35 lm) for 58Ni projectile at 7.92 MeV energy. The energy where the etching threshold (dE/dX(Elec.) = 3.4 keV/nm) reached is different for each ions. In case of 197Au ion, the etching threshold reached at 12.09 MeV, while its value is very low for other chosen projectiles. The value of dE/dX(Nucl.) (at dE/ dX(Elec.) = 3.4 keV/nm) is minimum (0.13 keV/nm) for 58Ni projectile and maximum (2.68 keV/nm) for 238U projectile.
Table 4 Various parameters at etching threshold [dE/dX(Elec.) = (3.4 keV/nm)] (using SRIM 08.04 [17]) for different heavy ions in muscovite mica. Ion
Energy (MeV)
dE/dX(Nucl.) (keV/nm)
Range correction factor (lm)
Ni Nb Xe Au Pb Bi U
7.92 8.27 8.02 12.09 6.01 5.86 6.00
0.13 0.35 0.72 1.32 2.13 2.20 2.68
4.35 3.08 2.33 2.44 1.10 1.06 1.00
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5
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
16
3 2
14
1
12
0 3
10
% Deviation
dE/dX (Nucl.)
RCF (µm)
4
2 1
6 4
0
2
-1
0 -2
12
E(MeV)
8
30
40
50
60
70
80
Dip Angle (Deg)
10
Fig. 3b. The range deficit [%] between experimental(corrected) [7] and calculated [17,20] ranges of 93Nb (18.00 MeV/n) ion in muscovite mica as a function of dip angle.
8 6 Ni
Nb
Xe
Au
Pb
Bi
U
Ions Fig. 2. Various parameters at etching threshold [dE/dX(Elec.) = 3.4 keV/nm] for different ions in muscovite mica.
For 58Ni (11.56 MeV/n) ion, it is clear from Table 3 that, the range values calculated using LISE++:0-[Hub90] formulation show minimum deviation (8%) from the corrected experimental values [7] as compared to the other adopted formulations (SRIM shows maximum deviation of 11%). Fig. 3a presents the dip angle (30°–75°) behaviour of the experimental [7] and calculated [17,20] range values of 93Nb (18.00 MeV/n) ion in muscovite mica. Fig. 3b shows the dip angle
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
160
100
158 156 154
80
152
Range (µm)
Range (µm)
150 148 146 144
60
40
142
20
140 138
0
136 134 30
40
50
60
70
80
Dip Angle (Deg) Fig. 3a. Dip angle dependence of experimental [7] and the calculated [17,20] range values of 93Nb (18.00 MeV/n) ions in muscovite mica.
0
2
4
6
8
10
12
14
Energy (MeV/u) Fig. 4a. Energy behaviour of experimental [33] and calculated [17,20] range values of 129Xe ions incident at 45° in muscovite mica.
M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
40
% Deviation
114 112 110 108 106 104 102 100 98 96 94 92 90 30
35
40
45
50
55
60
Dip Angle (Deg) Fig. 5a. Variation of experimental [30] and calculated [17,20] range values of 132Xe (12.50 MeV/n) ions with incident angle in muscovite mica.
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
6 4 2 0 -2 -4 -6 -8 -10 -12 -14
30
-16
20
-18 -20
10
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
116
Range (µm)
behaviour of the percentage deviations of the calculated 93Nb ion range values from the corrected experimental data. It is clear from these observations that the experimental and calculated range values for 93Nb (18.00 MeV/n) ion show overall good agreement (1%) at high dip angle (75°) and show maximum deviation at low dip angles. Among various adopted procedures for range calculation, the LISE++:0-[Hub90] code shows good results as compared to other formulations. Fig. 4a shows the energy (0.50–13.04 MeV/u) behaviour of the experimental [33] and the calculated [17,20] range values of 129 Xe ion in muscovite mica at incident angle of 45°. Fig. 4b shows the energy behaviour of the percentage deviations of the calculated 129 Xe ion range values from the corrected experimental range data. In this case, it is clear that the percentage deviation between the calculated and experimetal range values decreases as the incident energy of the 129Xe ion increases. At high energy (13.04 MeV/u), there is a good agreement [about 0% deviation for LISE++:8.3.107–3-ATIMA1.2 (Without LS correction) formulation] between calculated and experimental range values. At low energy (0.5 MeV/u and 0.15 MeV/u), there is large deviation (about 51%) between the caculated and experimental range values. The dip angle (30°–60°) dependance of the experimental [30] and calculated [17,20] range values of 132Xe (12.50 MeV/n) ions in muscovite mica detector is presented in Fig. 5a. Fig. 5b shows the dip angle behaviour of the percentage deviations of the calculated 132Xe ion range values from the corrected experimental range data. These results make clear that, for 132Xe (12.50 MeV/n) ion, the calculated range values at low dip angle show overall good agreement [1% for LISE++:8.3.107–2-ATIMA1.2 (LS Theory) and LISE++:8.3.107–3-ATIMA1.2 (Without LS correction) formulations] with the experimental data as compared to high dip angle range values (18% for SRIM). Among all the adopted formulations of range calculation, the LISE++:1-[Zie85] code shows good results for all these dip angles (30°–60°) as compared to other choosen procedures. For 179Au ion, it is clear from Figs. 6a,b that the LISE++:0[Hub90] formulation presents overall good agreement between the calculated and exprimentally measured range values as
% Deviation
2622
30
35
40
45
50
55
60
Dip Angle (Deg)
0
Fig. 5b. The range deficit [%] between experimental(corrected) [30] and calculated [17,20] ranges of 132Xe (12.50 MeV/n) ions in muscovite mica as a function of dip angle.
-10 -20 -30 -40 -50 -60
0
2
4
6
8
10
12
14
Energy (MeV/u) Fig. 4b. The range deficit [%] between experimental(corrected) [33] and calculated [17,20] ranges of 129Xe ions in muscovite mica as a function of specific energy [MeV/u].
compared to the other adopted formulations in the given energy region (11.40–15.69 MeV/n). For 208Pb projectile ranges [7,31] in muscovite mica at dip angle of 45° (from Table 3), the LISE++:0-[Hub90] formulation tabulates good range values and show minimum range deficit as compared to other codes. The range deficit is minimum for high energy (17.12 MeV/n) as compared to low energy (13.80 MeV/n) 208Pb ion. The variation of the experimental [30] and calculated [17,20] range values for 209Bi (13.01 MeV/n) ions in muscovite mica detector with dip angle (15°–75°) is presented in Fig. 7a. Fig. 7b shows
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M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction) 108
125
106
120
104
115
102
110
100
Range (µm)
Range (µm)
130
105 100 95
98 96 94
90
92 85
90 80
88 75 11
12
13
14
15
16
10
20
30
Energy (MeV/n)
50
60
70
80
Fig. 7a. Dip angle behaviour of experimental [32] and calculated [17,20] range values of 209Bi (13.01 MeV/n) heavy ions in muscovite mica.
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
20 18 16 14 12 10
% Deviation
% Deviation
Fig. 6a. Energy behaviour of experimental [7] and calculated [17,20] range values of 179Au heavy ions incident at 45° angle in muscovite mica.
21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3
40
Dip Angle (Deg)
8 6 4 2 0 -2 -4 -6 -8
11
12
13
14
15
16
Energy (MeV/n) Fig. 6b. The range deficit [%] between experimental(corrected) [7] and calculated [17,20] ranges of 179Au ions in muscovite mica as a function of specific energy [MeV/n].
the dip angle behaviour of percentage deviations of the calculated 209 Bi ion range values from the experimental measured range data. It is clear from these observations that the deficit between the calculated and experimental range values decreases [0% in case of LISE++:8.3.107–2-ATIMA1.2 (LS Theory)] towards higher dip angle [75°] as compared to low dip angle [18% for SRIM at 15°]. Among
10
20
30
40
50
60
70
80
Dip Angle (Deg) Fig. 7b. The range deficit [%] between experimental(corrected) [32] and calculated [17,20] ranges of 209Bi (13.01 MeV/n) ions in muscovite mica as a function of dip angle.
all the adopted procedures of range calculation, the LISE++:0[Hub90] formulation shows overall good results at all dip angles (15°–75°) as compared to other choosen codes. Fig. 8a presents the dip angle (30°–75°) dependance of the experimental [7] and calculated [17,20] range values of 238U (10.00 MeV/n) ion in muscovite mica. Fig. 8b shows the dip angle
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M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
88
Experimental Range Corrected Experimental Range SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
140 130
86 84
120
82
110
80
100
Range (µm)
Range (µm)
78 76 74 72
90 80 70
70
60
68 66
50
64
40
62
6 30
40
50
60
70
8
80
10
12
14
16
Energy (MeV/n)
Dip Angle (Deg) Fig. 8a. Dip angle behaviour of experimental [7] and calculated [17,20] range values of 238U (10.00 MeV/n) heavy ions in muscovite mica.
Fig. 9a. Energy behaviour of experimental [7] and calculated [17,20] range values of 238U heavy ions incident at 45° angle in muscovite mica.
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
SRIM-08.04 LISE++:8.3.107-0-[Hub90] LISE++:8.3.107-1-[Zie85] LISE++:8.3.107-2-ATIMA1.2 (LS Theory) LISE++:8.3.107-3-ATIMA1.2 (Without LS correction)
30 28 26
35
24 30
% Deviation
22
% Deviation
25 20 15
20 18 16 14
10
12 10
5
8 0
6
8
10
12
14
16
Energy (MeV/n)
-5 30
40
50
60
70
80
Dip Angle (Deg)
Fig. 9b. The range deficit [%] between experimental(corrected) [7] and calculated [17,20] ranges of 238U ions in muscovite mica as a function of specific energy [MeV/n].
Fig. 8b. The range deficit [%] between experimental(corrected) [7] and calculated [17,20] ranges of 238U (10.00 MeV/n) ion in muscovite mica as a function of dip angle.
behaviour of percentage deviations of the calculated 238U ion range values from the experimentally measured range data. For 238U (10.00 MeV/n) ion projectile, the percentage deviation between the calculated and experimental range values decreases as the angle of incidence increases. LISE++:0-[Hub90] tabulated range values show overall good agreement for all choosen dip angles
(30°–75°) as compared to the rest of the formulations. It is also clear from Figs. 9a,b that the percentage deviation between the calculated and experimental range values decreases as the incident energy of the 238U ion (dip angle of 45°) increases. At high energy, there is a good agreement between LISE++:0-[Hub90] formulation tabulated and experimental range values. At low energy, there is large deviation between the caculated and experimental range values.
M. Singh et al. / Nuclear Instruments and Methods in Physics Research B 268 (2010) 2617–2625
From all these observations, it is interesting to note that the heavy ion range values calculated using all the adopted formulations deviate significantly from the experimentally measured data in muscovite mica. This might be due to the reasons that the procedures involved in most of the present theoretical and semiempirical stopping formulations are not dip angle dependent. The dip angle dependent stopping processes might be due to inhomogeneity of various properties of the detectors in different orientations. The penetrating projectile observes different interaction processes in different orientation of the materials, thus it covers different path in different directions. 6. Conclusion The experimental observations lead to the conclusion that most of the available procedures for range and energy loss calculation of ions do not account the anisotropic effect on stopping processes in layered crystalline materials like mica. The dip angle dependent stopping parameters can play significant role in ion stopping ideas in this type of complex structures. These types of crystalline materials are made up of three-dimensional array of atoms arranged in an orderly fashion, and the ion movement is very much directional dependent. The physical (absorbance, refractive index, magnetic field, density, etc.), mechanical (frictional forces, elastic moduli etc.) and chemical properties (different atomic and bonding environs) often differ with orientation in these types of materials and in relation to these properties, atoms are able to distort one another easier in some directions than others. The dip angle dependent stopping processes might be due to inhomogeneity of these properties of the detectors in different orientations. The ionic field of the penetrating projectile exerts different action (interaction processes) in different orientation of the crystalline materials, thus the anisotropic ion energy loss consumes different intensity. When the stopping medium is anisotropic or inhomogeneous, the finite geometrical dimensions of the material cannot be ignored or minimised and the detailed geometric modeling of ion propagation through these types of diverse materials (like mica) is required. It is strongly recommended that the stopping parameters affected by the anisotropic structure of the detecting materials should be studied and analysed for better calculations of various heavy ion stopping processes in crystalline media. Acknowledgments One of the authors (M. Singh) is thankful to the Council of Scientific and Industrial Research (CSIR, India) for Research Associateship. References [1] [2] [3] [4] [5] [6] [7] [8]
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