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Chemical effects in the stopping cross sections of protons in rare earth fluorides
NIM B Beam Interactions with Materials & Atoms
Nuclear Instruments and Methods in Physics Research B 254 (2007) 39–42 www.elsevier.com/locate/nimb
Chemical effects in the stopping cross sections of protons in rare earth fluorides J. Miranda *, J.C. Pineda Instituto de Fı´sica, Universidad Nacional Auto´noma de Me´xico, Apartado Postal 20-364, 01000 Me´xico, D. F., Mexico Received 20 September 2006; received in revised form 10 October 2006 Available online 27 November 2006
Abstract Stopping cross sections were measured for 0.5–0.7 MeV protons impinging on selected rare earth fluorides using energy differences of ions backscattered by thin films. The surface approximation was employed to determine the stopping cross sections. Consideration of chemical effects through the enthalpy of formation of the target compounds, as suggested by Bauer and Semrad (Nucl. Instr. and Meth. B 182 (2001) 62), allows a much better agreement with the electronic stopping predictions of the SRIM code, the Montenegro et al. universal formula and the tables by Janni. Ó 2006 Elsevier B.V. All rights reserved. PACS: 34.50.Bw; 61.66.Fn; 82.80.Yc Keywords: Stopping cross section; Protons; Rare earth fluorides; Chemical effects
1. Introduction The stopping of ions in matter is currently an issue of great interest. Prediction of the stopping power for a particular ion in a given target, especially when it is a compound, is very important for areas such as ion beam modification of materials, medical physics and ion beam analysis (IBA) applications [1]. Theories trying to explain the stopping power for light ions are relatively well-developed [2,3] and there are also many efforts to measure this magnitude for a wide variety of ion-target combinations. In particular, several methods exist that allow the calculation of stopping power of protons interacting with pure elements or other substances. Among them, it is possible to mention the computer code SRIM [4], the ‘‘universal’’ formula published by Montenegro et al. [5,6], or the tables published by Janni [7]. The use of SRIM [4] is widely known among the IBA community, so no further comments about it are considered necessary here. In contrast, the Montene*
Corresponding author. Tel.: +52 55 56225002; fax: +52 55 56225009. E-mail address: miranda@fisica.unam.mx (J. Miranda).
0168-583X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.10.065
gro et al. formula is based on the probabilistic character of the stopping cross section, i.e. the fact that there are different processes participating in the energy loss phenomenon more or less predominantly, according to their occurrence probability. In this model the stopping curve is divided in two regions: the high velocity regime, i.e. ionization and those associated with all the other degrees of freedom occurring in the low velocity region [5]. Here, the authors postulate that the electronic stopping cross section for the whole velocity range is due to those events and so they constructed their stopping power formula based on this postulate and some reasonable physical assumptions [5,6]. Finally, the tables by Janni [7] are based on both experimental results (for the intermediate energy range) and on theoretical calculations (for the low and high energy intervals). When the stopping power of ions in compounds is considered, it is usually assumed that Bragg’s additive rule can be applied to obtain this magnitude from the stopping cross section of the pure elements [8]. However, experimental deviations from these predictions have been observed for many compounds, so further approximations are required to explain those disagreements [9]. For instance,
40
J. Miranda, J.C. Pineda / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 39–42
the effect of chemical binding makes Bragg’s rule not applicable to every substance. This may be the case of rare earth fluorides, which normally have the form RF3, where R represents the rare earth element. No available experimental data exist for the stopping power of protons or other ions in these compounds. One of the approaches followed to improve the calculations of stopping cross sections in compounds was suggested by Bauer and Semrad [10]. They propose an adjustment to the stopping cross sections obtained through Bragg’s rule, based on the enthalpy of formation of the compound (in their work, the authors also mentioned a correction to predict stopping cross section for different physical states). Thus, if DH is the enthalpy of formation of the compound, Imixt is the average ionization energy of the elements as a mixture (used to apply directly Bragg’s rule), emixt and ecomp are the stopping cross section for the mixture of pure elements and the compound, respectively, then the correction to the stopping cross section DeCS is given by [11] 4pZ 21 Z 2 e4 DH ln 1 þ DeCS emixt ecomp ¼ I mixt mv2
4pZ 21 Z 2 e4 DH I mixt mv2
;
ð1Þ
where Z1 is the atomic number of the incoming ion, Z2 is the number of electrons in the target atoms, e is the electron charge, m is the electron mass and v is the ion velocity. For the rare earth fluorides, it is observed that DH has very high negative values, as compared to other compounds (see, for example, Fig. 2 in [10]). Thus, it is of interest to confirm if this approach can be applied to the stopping cross sections of protons in the aforementioned targets, testing the correction method under an unusual situation. With this in mind, in the present work the stopping cross sections of protons with energies between 0.5 and 0.7 MeV in rare earth fluorides targets were measured and the results compared with the predictions offered by SRIM, the Montenegro et al. formula and the tables published by Janni, including the chemical binding correction suggested by Bauer and Semrad. 2. Experimental Samples were prepared as thin films of rare earths fluorides (Nd, Sm, Gd and Ho) deposited by evaporation onto pyrolytic graphite substrates (Ernest F. Fullam, Latham, NY, USA). The advantage of using these substrates is that they have a very high purity and present a very smooth surface [11]. Only for a few rare earth fluorides it is possible to find values of the enthalpy of formation in the literature [12]; these four compounds are in this group. The DH values are given in Table 1. The proton beams were produced by the 0.7 MV Van de Graaff accelerator at the Instituto de Fı´sica, UNAM, Mexico. Proton energies varied from 0.50 to 0.70 MeV, in 0.02 MeV steps. The experimental setup is
Table 1 Enthalpy of formation [12] and thicknesses of the rare earth fluorides films used in the present work Compound
Enthalpy of formation (eV/molecule)
Film thickness (lg cm2)
NdF3 SmF3 GdF3 HoF3
17.17 18.43 13.44 17.69
45.2 40.0 45.7 33.0
(2.3) (2.0) (2.3) (1.6)
sketched in Fig. 1. The backscattered particles were registered with a Canberra PIPS detector placed at an angle of 155°, while the resulting spectra were collected using an ORTEC multichannel analyzer add-in board attached to a personal computer. The film thickness was measured using the X-ray La line of the corresponding rare earth element, through a comparison with the number of X-ray photons emitted by MicroMatter thin film standards of the same rare earth fluorides (nominal thickness around 50 lg cm2), assuming that the X-ray attenuation and stopping is of the same order in all the similar targets. The measured thicknesses are also shown in Table 1. The X-rays were induced by a 0.70 MeV proton beam and the photons were registered with a Si(Li) detector, placed at an angle of 90° from the direction of the incident beam. In the present work, the proton energy loss was measured using the surface energy approximation [8] ½e0 ðK= cos h1 Þ þ ð1= cos h2 Þ
ð2Þ
ð1= cos h1 Þ þ ð1= cos h2 Þ KE0 : ðK= cos h1 Þ þ ð1= cos h2 Þ
ð3Þ
eðEx Þ ¼ and Ex ¼
Here, e(Ex) is the stopping cross section at the energy Ex; [e0] is the stopping cross section factor for the incident energy E0 [8]; Ex is an intermediate energy between the incident and final energy of the ions after the backscattering process; K is the kinematic factor and h1 and h2 are the incident and outgoing angles of the backscattered particle, respectively, as seen in Fig. 2. In this experiment, h1 = 45° and h2 = 25°. The most important factors contributing to the uncertainty in the stopping cross sections measurement are the film thickness of the MicroMatter standards (quoted as 5%); the statistical uncertainty in the La X-rays for the thickness measurement (less than 1%); the uncertainty in the energy calibration of the spectra (obtained through the high energy edge of the rare earth element signal in the backscattering spectra) and the resolution of the detection system. Moreover, some error in the stopping cross sections might be expected, although it was not quantified, due to the surface energy approximation mentioned above. 3. Results and discussion The measured stopping cross sections per atom for all the compounds are displayed in Table 2. Figs. 3–6 show
J. Miranda, J.C. Pineda / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 39–42
41
X-ray Detector
Van de Graaff Accelerator
Switching Magnet
Target
Particle Detector
Scattering Chamber
A
Nuclear Electronics Current Integrator
Multichannel Analyzer
Fig. 1. Diagram of the experimental setup for the measurement of stopping cross sections. 15
PIPS Detector Thin Film Target
NdF 3
Experimental MCV MCV Corr SRIM SRIM Corr Janni Janni Corr
ε (1015 eV/[at cm-2])
14
θ2 Proton Beam E0
θ1
13
12
11
10
Fig. 2. Diagram of the geometry for the measurement of stopping cross sections.
9
the comparison of the experimental values with the predictions given by SRIM, Montenegro et al. and Janni, before and after adjusting by the Bauer-Semrad method. The ionization energies given by Montenegro et al. [5] were used to calculate both the stopping cross sections and the correction. Unfortunately, there are no other experimental data to establish an evaluation of the quality of the results. Nevertheless, the improvement in the calculations by the three methods is apparent, although it is not possible, due to the experimental uncertainty, to make a statement about which of the three methods provides the most reliable predictions. Results for HoF3 present the largest disagreement from the
8 0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
Proton energy (MeV) Fig. 3. Stopping cross sections per atom of protons incident on NdF3 films. The curves correspond to the SRIM computer code [5], MCV to the Montenegro et al. formula [6] and the tables published by Janni [7]. The curves with the ‘‘Corr’’ legend are associated to the values corrected by chemical effects according to the Bauer and Semrad model [10].
theoretical estimates, in particular for higher energies. This might be explained because this film was the thinnest among all the samples (see Table 1) and the spectra for that
Table 2 Stopping cross sections per atom (1015eV/(at cm2))measured in rare earth fluorides Proton energy (MeV) 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 a
NdF3 10.6 10.6 10.1 10.2 10.2 9.91 10.2 9.97 9.91 9.84 9.37
SmF3 a
(0.9) (0.8) (0.8) (0.8) (0.8) (0.79) (0.8) (0.80) (0.79) (0.79) (0.75)
10.8 10.7 10.4 10.6 11.0 10.9 9.84 10.3 9.92 10.1 9.76
Numbers between parenthesis represent the experimental uncertainty.
GdF3 (0.9) (0.9) (0.8) (0.8) (0.9) (0.9) (0.79) (0.8) (0.79) (0.8) (0.78)
11.1 11.3 11.2 11.1 11.1 11.0 10.9 11.3 11.2 10.9 10.9
HoF3 (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8)
11.5 11.0 10.5 10.3 10.1 9.84 9.62 8.87 8.92 8.44 8.48
(0.9) (0.9) (0.8) (0.8) (0.8) (0.79) (0.77) (0.71) (0.71) (0.67) (0.68)
42
J. Miranda, J.C. Pineda / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 39–42 15
15
SmF3
Experimental MCV MCV Corr SRIM SRIM Corr Janni Janni Corr
13
12
14
ε (1015 eV/[at cm-2])
ε (1015 eV/[at cm-2])
14
11
HoF3
Experimental MCV MCV Corr SRIM SRIM Corr Janni Janni Corr
13 12 11 10
10 9 9
8
8 0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
7 0.45
0.50
Proton energy (MeV)
0.55
0.60
0.65
0.70
0.75
0.80
Proton energy (MeV)
Fig. 4. Same as Fig. 3, but for SmF3 films.
Fig. 6. Same as Fig. 3, but for HoF3 films.
15
GdF3 14
ε (1015 eV/[at cm-2])
more, other ion-target combinations should also be studied. In any case, the reduction of experimental uncertainties is strongly required, to establish if the observed differences among the models or tables are truly significant. Predictions of all the methods are close one to another, thus making it possible to use any of them for practical purposes. However, it should be stressed that the simplicity of the Montenegro et al. formula makes it very adequate for its inclusion in computer codes for IBA applications (such as Rutherford Backscattering or Particle Induced X-ray Emission).
Experimental MCV MCV Corr SRIM SRIM Corr Janni Janni Corr
13
12
11
10
9 0.45
Acknowledgements 0.50
0.55
0.60
0.65
0.70
0.75
0.80
Proton energy (MeV) Fig. 5. Same as Fig. 3, but for GdF3 films.
energy range were more difficult to analyze. It must be noted that, as the enthalpies of formation for all these compounds are negative, the corrected values lie below the direct Bragg’s rule evaluation of the stopping cross sections. The consideration of the chemical effects by the Bauer-Semrad [10] approach seems to go in the right direction for this study, in spite of its simplicity. The major drawback of the method is that enthalpies of formation are not currently available for all the compounds that might be of interest in a particular study. 4. Conclusions The results of the comparison between experimental data and those from theoretical or semi-empirical models suggest that more measurements are needed, to test the validity of those methods, extending the range of energies above and below those used in the present work. Further-
The authors thank the technical assistance of J. Galindo and M. Galindo. This work was supported in part by CONACyT, under contract 40122-F. References [1] H. Paul, A. Schinner, Nucl. Instr. and Meth. B 249 (2006) 1. [2] J.F. Ziegler, J. Appl. Phys. Rev. Appl. Phys. 85 (1999) 1249. [3] S. Heredia-Avalos, R. Garcia-Molina, J.M. Ferna´ndez-Varea, I. Abril, Phys. Rev. A 72 (2005) (paper 052902). [4] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Solids, second ed., Pergamon Press, New York, 1999. [5] E.C. Montenegro, S.A. Cruz, C. Vargas-Aburto, Phys. Lett. 92A (1982) 195. [6] C. Vargas-Aburto, S.A. Cruz, E.C. Montenegro, Radiat. Effects 80 (1984) 23. [7] J.F. Janni, At. Data Nucl. Data Tab. 27 (1982) 147. [8] W.K. Chu, J.W. Mayer, M.A. Nicolet, Backscattering Spectrometry, Academic Press, New York, 1978. [9] J.F. Ziegler, Nucl. Instr. and Meth. B 219–220 (2004) 1027. [10] P. Bauer, D. Semrad, Nucl. Instr. and Meth. B 182 (2001) 62. [11] M. Lugo-Licona, J. Miranda, C.M. Romo-Kro¨ger, J. Radioanal. Nucl. Chem. 262 (2004) 391. [12] Handbook of Chemistry and Physics, seventy second ed., CRC Press, Boca Raton, FL, USA, 1991–1992. p. 5/16.
Nuclear Instruments and Methods in Physics Research B 254 (2007) 39–42 www.elsevier.com/locate/nimb
Chemical effects in the stopping cross sections of protons in rare earth fluorides J. Miranda *, J.C. Pineda Instituto de Fı´sica, Universidad Nacional Auto´noma de Me´xico, Apartado Postal 20-364, 01000 Me´xico, D. F., Mexico Received 20 September 2006; received in revised form 10 October 2006 Available online 27 November 2006
Abstract Stopping cross sections were measured for 0.5–0.7 MeV protons impinging on selected rare earth fluorides using energy differences of ions backscattered by thin films. The surface approximation was employed to determine the stopping cross sections. Consideration of chemical effects through the enthalpy of formation of the target compounds, as suggested by Bauer and Semrad (Nucl. Instr. and Meth. B 182 (2001) 62), allows a much better agreement with the electronic stopping predictions of the SRIM code, the Montenegro et al. universal formula and the tables by Janni. Ó 2006 Elsevier B.V. All rights reserved. PACS: 34.50.Bw; 61.66.Fn; 82.80.Yc Keywords: Stopping cross section; Protons; Rare earth fluorides; Chemical effects
1. Introduction The stopping of ions in matter is currently an issue of great interest. Prediction of the stopping power for a particular ion in a given target, especially when it is a compound, is very important for areas such as ion beam modification of materials, medical physics and ion beam analysis (IBA) applications [1]. Theories trying to explain the stopping power for light ions are relatively well-developed [2,3] and there are also many efforts to measure this magnitude for a wide variety of ion-target combinations. In particular, several methods exist that allow the calculation of stopping power of protons interacting with pure elements or other substances. Among them, it is possible to mention the computer code SRIM [4], the ‘‘universal’’ formula published by Montenegro et al. [5,6], or the tables published by Janni [7]. The use of SRIM [4] is widely known among the IBA community, so no further comments about it are considered necessary here. In contrast, the Montene*
Corresponding author. Tel.: +52 55 56225002; fax: +52 55 56225009. E-mail address: miranda@fisica.unam.mx (J. Miranda).
0168-583X/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2006.10.065
gro et al. formula is based on the probabilistic character of the stopping cross section, i.e. the fact that there are different processes participating in the energy loss phenomenon more or less predominantly, according to their occurrence probability. In this model the stopping curve is divided in two regions: the high velocity regime, i.e. ionization and those associated with all the other degrees of freedom occurring in the low velocity region [5]. Here, the authors postulate that the electronic stopping cross section for the whole velocity range is due to those events and so they constructed their stopping power formula based on this postulate and some reasonable physical assumptions [5,6]. Finally, the tables by Janni [7] are based on both experimental results (for the intermediate energy range) and on theoretical calculations (for the low and high energy intervals). When the stopping power of ions in compounds is considered, it is usually assumed that Bragg’s additive rule can be applied to obtain this magnitude from the stopping cross section of the pure elements [8]. However, experimental deviations from these predictions have been observed for many compounds, so further approximations are required to explain those disagreements [9]. For instance,
40
J. Miranda, J.C. Pineda / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 39–42
the effect of chemical binding makes Bragg’s rule not applicable to every substance. This may be the case of rare earth fluorides, which normally have the form RF3, where R represents the rare earth element. No available experimental data exist for the stopping power of protons or other ions in these compounds. One of the approaches followed to improve the calculations of stopping cross sections in compounds was suggested by Bauer and Semrad [10]. They propose an adjustment to the stopping cross sections obtained through Bragg’s rule, based on the enthalpy of formation of the compound (in their work, the authors also mentioned a correction to predict stopping cross section for different physical states). Thus, if DH is the enthalpy of formation of the compound, Imixt is the average ionization energy of the elements as a mixture (used to apply directly Bragg’s rule), emixt and ecomp are the stopping cross section for the mixture of pure elements and the compound, respectively, then the correction to the stopping cross section DeCS is given by [11] 4pZ 21 Z 2 e4 DH ln 1 þ DeCS emixt ecomp ¼ I mixt mv2
4pZ 21 Z 2 e4 DH I mixt mv2
;
ð1Þ
where Z1 is the atomic number of the incoming ion, Z2 is the number of electrons in the target atoms, e is the electron charge, m is the electron mass and v is the ion velocity. For the rare earth fluorides, it is observed that DH has very high negative values, as compared to other compounds (see, for example, Fig. 2 in [10]). Thus, it is of interest to confirm if this approach can be applied to the stopping cross sections of protons in the aforementioned targets, testing the correction method under an unusual situation. With this in mind, in the present work the stopping cross sections of protons with energies between 0.5 and 0.7 MeV in rare earth fluorides targets were measured and the results compared with the predictions offered by SRIM, the Montenegro et al. formula and the tables published by Janni, including the chemical binding correction suggested by Bauer and Semrad. 2. Experimental Samples were prepared as thin films of rare earths fluorides (Nd, Sm, Gd and Ho) deposited by evaporation onto pyrolytic graphite substrates (Ernest F. Fullam, Latham, NY, USA). The advantage of using these substrates is that they have a very high purity and present a very smooth surface [11]. Only for a few rare earth fluorides it is possible to find values of the enthalpy of formation in the literature [12]; these four compounds are in this group. The DH values are given in Table 1. The proton beams were produced by the 0.7 MV Van de Graaff accelerator at the Instituto de Fı´sica, UNAM, Mexico. Proton energies varied from 0.50 to 0.70 MeV, in 0.02 MeV steps. The experimental setup is
Table 1 Enthalpy of formation [12] and thicknesses of the rare earth fluorides films used in the present work Compound
Enthalpy of formation (eV/molecule)
Film thickness (lg cm2)
NdF3 SmF3 GdF3 HoF3
17.17 18.43 13.44 17.69
45.2 40.0 45.7 33.0
(2.3) (2.0) (2.3) (1.6)
sketched in Fig. 1. The backscattered particles were registered with a Canberra PIPS detector placed at an angle of 155°, while the resulting spectra were collected using an ORTEC multichannel analyzer add-in board attached to a personal computer. The film thickness was measured using the X-ray La line of the corresponding rare earth element, through a comparison with the number of X-ray photons emitted by MicroMatter thin film standards of the same rare earth fluorides (nominal thickness around 50 lg cm2), assuming that the X-ray attenuation and stopping is of the same order in all the similar targets. The measured thicknesses are also shown in Table 1. The X-rays were induced by a 0.70 MeV proton beam and the photons were registered with a Si(Li) detector, placed at an angle of 90° from the direction of the incident beam. In the present work, the proton energy loss was measured using the surface energy approximation [8] ½e0 ðK= cos h1 Þ þ ð1= cos h2 Þ
ð2Þ
ð1= cos h1 Þ þ ð1= cos h2 Þ KE0 : ðK= cos h1 Þ þ ð1= cos h2 Þ
ð3Þ
eðEx Þ ¼ and Ex ¼
Here, e(Ex) is the stopping cross section at the energy Ex; [e0] is the stopping cross section factor for the incident energy E0 [8]; Ex is an intermediate energy between the incident and final energy of the ions after the backscattering process; K is the kinematic factor and h1 and h2 are the incident and outgoing angles of the backscattered particle, respectively, as seen in Fig. 2. In this experiment, h1 = 45° and h2 = 25°. The most important factors contributing to the uncertainty in the stopping cross sections measurement are the film thickness of the MicroMatter standards (quoted as 5%); the statistical uncertainty in the La X-rays for the thickness measurement (less than 1%); the uncertainty in the energy calibration of the spectra (obtained through the high energy edge of the rare earth element signal in the backscattering spectra) and the resolution of the detection system. Moreover, some error in the stopping cross sections might be expected, although it was not quantified, due to the surface energy approximation mentioned above. 3. Results and discussion The measured stopping cross sections per atom for all the compounds are displayed in Table 2. Figs. 3–6 show
J. Miranda, J.C. Pineda / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 39–42
41
X-ray Detector
Van de Graaff Accelerator
Switching Magnet
Target
Particle Detector
Scattering Chamber
A
Nuclear Electronics Current Integrator
Multichannel Analyzer
Fig. 1. Diagram of the experimental setup for the measurement of stopping cross sections. 15
PIPS Detector Thin Film Target
NdF 3
Experimental MCV MCV Corr SRIM SRIM Corr Janni Janni Corr
ε (1015 eV/[at cm-2])
14
θ2 Proton Beam E0
θ1
13
12
11
10
Fig. 2. Diagram of the geometry for the measurement of stopping cross sections.
9
the comparison of the experimental values with the predictions given by SRIM, Montenegro et al. and Janni, before and after adjusting by the Bauer-Semrad method. The ionization energies given by Montenegro et al. [5] were used to calculate both the stopping cross sections and the correction. Unfortunately, there are no other experimental data to establish an evaluation of the quality of the results. Nevertheless, the improvement in the calculations by the three methods is apparent, although it is not possible, due to the experimental uncertainty, to make a statement about which of the three methods provides the most reliable predictions. Results for HoF3 present the largest disagreement from the
8 0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
Proton energy (MeV) Fig. 3. Stopping cross sections per atom of protons incident on NdF3 films. The curves correspond to the SRIM computer code [5], MCV to the Montenegro et al. formula [6] and the tables published by Janni [7]. The curves with the ‘‘Corr’’ legend are associated to the values corrected by chemical effects according to the Bauer and Semrad model [10].
theoretical estimates, in particular for higher energies. This might be explained because this film was the thinnest among all the samples (see Table 1) and the spectra for that
Table 2 Stopping cross sections per atom (1015eV/(at cm2))measured in rare earth fluorides Proton energy (MeV) 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 a
NdF3 10.6 10.6 10.1 10.2 10.2 9.91 10.2 9.97 9.91 9.84 9.37
SmF3 a
(0.9) (0.8) (0.8) (0.8) (0.8) (0.79) (0.8) (0.80) (0.79) (0.79) (0.75)
10.8 10.7 10.4 10.6 11.0 10.9 9.84 10.3 9.92 10.1 9.76
Numbers between parenthesis represent the experimental uncertainty.
GdF3 (0.9) (0.9) (0.8) (0.8) (0.9) (0.9) (0.79) (0.8) (0.79) (0.8) (0.78)
11.1 11.3 11.2 11.1 11.1 11.0 10.9 11.3 11.2 10.9 10.9
HoF3 (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8) (0.8)
11.5 11.0 10.5 10.3 10.1 9.84 9.62 8.87 8.92 8.44 8.48
(0.9) (0.9) (0.8) (0.8) (0.8) (0.79) (0.77) (0.71) (0.71) (0.67) (0.68)
42
J. Miranda, J.C. Pineda / Nucl. Instr. and Meth. in Phys. Res. B 254 (2007) 39–42 15
15
SmF3
Experimental MCV MCV Corr SRIM SRIM Corr Janni Janni Corr
13
12
14
ε (1015 eV/[at cm-2])
ε (1015 eV/[at cm-2])
14
11
HoF3
Experimental MCV MCV Corr SRIM SRIM Corr Janni Janni Corr
13 12 11 10
10 9 9
8
8 0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
7 0.45
0.50
Proton energy (MeV)
0.55
0.60
0.65
0.70
0.75
0.80
Proton energy (MeV)
Fig. 4. Same as Fig. 3, but for SmF3 films.
Fig. 6. Same as Fig. 3, but for HoF3 films.
15
GdF3 14
ε (1015 eV/[at cm-2])
more, other ion-target combinations should also be studied. In any case, the reduction of experimental uncertainties is strongly required, to establish if the observed differences among the models or tables are truly significant. Predictions of all the methods are close one to another, thus making it possible to use any of them for practical purposes. However, it should be stressed that the simplicity of the Montenegro et al. formula makes it very adequate for its inclusion in computer codes for IBA applications (such as Rutherford Backscattering or Particle Induced X-ray Emission).
Experimental MCV MCV Corr SRIM SRIM Corr Janni Janni Corr
13
12
11
10
9 0.45
Acknowledgements 0.50
0.55
0.60
0.65
0.70
0.75
0.80
Proton energy (MeV) Fig. 5. Same as Fig. 3, but for GdF3 films.
energy range were more difficult to analyze. It must be noted that, as the enthalpies of formation for all these compounds are negative, the corrected values lie below the direct Bragg’s rule evaluation of the stopping cross sections. The consideration of the chemical effects by the Bauer-Semrad [10] approach seems to go in the right direction for this study, in spite of its simplicity. The major drawback of the method is that enthalpies of formation are not currently available for all the compounds that might be of interest in a particular study. 4. Conclusions The results of the comparison between experimental data and those from theoretical or semi-empirical models suggest that more measurements are needed, to test the validity of those methods, extending the range of energies above and below those used in the present work. Further-
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