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Lattice location of Cs atoms in cubic ZrO2 single crystals
Nuclear Instruments and Methods in Physics Research B 175±177 (2001) 453±457
www.elsevier.nl/locate/nimb
Lattice location of Cs atoms in cubic ZrO2 single crystals L. Thome a
a,*
, J. Jagielski
b,c
, A. Gentils a, F. Garrido
a
Centre de Spectrom etrie Nucl eaire et de Spectrom etrie de Masse, IN2P3-CNRS, B^ at. 108, 91405 Orsay, France b Institute of Electronic Materials Technology, Wolczynska 133, 01-919 Warsaw, Poland c The Andrzej Soltan Institute of Nuclear Studies, 05-400 Swierk/Otwock, Poland
Abstract The lattice location of a speci®c ®ssion product (Cs) implanted into cubic zirconia single crystals was investigated as a function of the atomic concentration by using Rutherford backscattering and channeling (RBS/C) experiments. At low concentration (<0.5 at.%), a signi®cant Cs substitutional fraction (0.5±0.6) is measured in channeling spectra recorded with the analyzing He beam aligned along the three main axes of the cubic crystal. Angular scans performed across the h1 0 0i axis indicate the formation of Cs-vacancy complexes. The ZrO2 single crystals are strongly damaged when the Cs concentration exceeds a few at.% and the Cs atoms are randomly located in the crystalline lattice. This latter result could be due to the precipitation of implanted Cs atoms. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 61.70.Vn; 61.80.Jh; 61.80.Mk Keywords: Doping and impurity implantation; Ion radiation eects; Channeling
1. Introduction Zirconium oxide (ZrO2 ) is a promising candidate as an inert matrix for the incineration of actinides originating from light-water reactors or dismounted nuclear weapons [1±3]. 1 Radiological-protection safety considerations lead to the study of the retention behaviour of radiotoxic isotopes (mostly ®ssion products) created in the material by nuclear reactions. Since the mobility of foreign species in a crystalline solid often depends *
Corresponding author. E-mail address: [email protected] (L. Thome). 1 For a review, see [1].
on their site in the host lattice, study of ®ssionproduct migration should include assessment of lattice location data. The present studies address such an issue. They rely on the determination by Rutherford backscattering and channeling (RBS/ C) experiments of the lattice sites of a speci®c ®ssion product (Cs) introduced in cubic ZrO2 single crystals by ion implantation. The in¯uence of several parameters, such as the radiation damage production and the ®ssion-product concentration, are also investigated. Besides their implications in the ®eld of nuclear waste management, the experiments reported in this paper deal with a more fundamental topic, namely the interaction between implanted ions and radiation defects.
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 0 ) 0 0 5 3 4 - 6
454
L. Thome et al. / Nucl. Instr. and Meth. in Phys. Res. B 175±177 (2001) 453±457
2. Experimental The samples used are cubic {1 0 0}-oriented ZrO2 single crystals stabilized with 9:5 mol% Y2 O3 . They were implanted at room temperature with 300 keV 133 Cs2 ions delivered by the IRMA implanter [4] of the CSNSM in Orsay. The maximum ion ¯uence was 1016 cm 2 , which led to Cs concentrations up to 3 at.% in the implanted layer. A current density lower than 1 lA cm 2 was used in order to prevent excessive target heating. The damage created in the crystalline lattice and the lattice site of implanted ions was determined by RBS/C experiments with a 3.06 MeV 4 He2 ion beam provided by the ARAMIS accelerator [5] of the CSNSM. This energy was chosen in order to take advantage of the resonant elastic scattering on 16 O at 3.045 MeV. A standard acquisition set-up with an energy resolution of about 10 keV was used. Prior to
the RBS analysis the samples were covered with a 10 nm-thick carbon layer to avoid sample charging. 3. Results and discussion Typical RBS/C spectra recorded on ZrO2 single crystals implanted with various ¯uences of Cs ions are presented in Fig. 1. The spectrum recorded in a random direction displays the Zr edge (channel 410), the O signal enhanced by the resonance (channel 160) and a tiny Cs peak (channel 425). The spectrum recorded on a virgin sample in the h1 0 0i axial direction exhibits a strong decrease of the RBS yield due to the channeling eect vmin 0:05. The h1 0 0i axial yield increases with increasing ion ¯uences, more particularly at the implantation depth (channel 400), due to the damage created by Cs ion implantation. The inset of Fig. 1 shows a zoom on the Cs peaks (after careful background subtraction)
Fig. 1. Random (full symbols) and h1 0 0i-aligned (open symbols) RBS spectra recorded on cubic ZrO2 single crystals implanted with various ¯uences of Cs ions. Squares: before implantation; circles: 5 1014 cm 2 ; triangles: 5 1015 cm 2 . The inset presents a zoom on the Cs peak (¯uence: 5 1014 cm 2 ).
L. Thome et al. / Nucl. Instr. and Meth. in Phys. Res. B 175±177 (2001) 453±457
for spectra recorded in h1 0 0i axial and random directions on the sample implanted at a ¯uence of 5 1014 cm 2 . These peaks were reproduced with Gaussian distributions; the values of the mean projected ranges and range stragglings extracted from the ®ts to the data are in agreement with those calculated with the TRIM Monte-Carlo simulation code [6]. A strong decrease of the peak area is observed in the case where the analyzing beam is aligned along the h1 0 0i axial direction, indicating that Cs atoms are partly shadowed by host atoms along this direction. An estimation of the fraction of Cs ions located in a substitutional position (with respect to the h1 0 0i axis), fS , can be obtained from the analysis of the Cs peaks in RBS/C spectra. The values of fS , taken as (1 vi ) (where vi is the channeling yield measured on the Cs peaks), are represented in Fig. 2 as a function of the Cs concentration (at the peak maximum). It is worth noting that formally (1 vi ) should be normalized by (1 vh ) in order to derive the actual substitutional fraction (vh is the channeling yield obtained on the Zr host at the implantation depth) [7]. However, this normalization which is valid for relatively small values of vh leads to unrealistic substitutional fractions (often higher than 1) in the case of a strongly disordered crystal. At low atomic concentration (i.e. for an implantation ¯uence of 5 1014 cm 2 ), fS is about
Fig. 2. Substitutional fraction for Cs ions implanted into cubic ZrO2 single crystals as a function of the Cs concentration.
455
0.5 and the correction to account for the disorder in the host matrix would lead to a value of 0.6. Fig. 2 shows that the value of fS decreases as the Cs concentration increases and reaches zero at about 3 at.%. Table 1 Substitutional fraction (fS ) measured along the three main axes for Cs ions implanted at a ¯uence of 5 1014 cm 2 into a cubic ZrO2 single crystal Axis
fS
h1 0 0i h1 1 0i h1 1 1i
0:53 0:07 0:55 0:07 0:60 0:07
Fig. 3. Angular scans across the h1 0 0i axis for Zr (®lled circles), O (open circles) and Cs (dotted triangles): (a) virgin crystal; (b) crystal implanted with 5 1014 cm 2 ; (c) crystal implanted with 5 1015 cm 2 .
456
L. Thome et al. / Nucl. Instr. and Meth. in Phys. Res. B 175±177 (2001) 453±457
The fraction of Cs atoms in fully substitutional sites (i.e. with respect to the various crystallographic orientations) can only be obtained by measuring the values of fS along the three main axial directions of the cubic ZrO2 lattice. Such values (not corrected by the host dechanneling) are reported in Table 1 for the sample implanted at low Cs concentration (¯uence: 5 1014 cm 2 ). The results show that the values of fS obtained along the three main axes lie in the range 0.5±0.6. This result con®rms that the actual fraction of Cs atoms lying in substitutional sites is around 60%. Additional information concerning the lattice location of implanted ions can be obtained by measuring the angular dependence of the backscattering yield through low-index axes. Fig. 3 presents angular scans across the h1 0 0i axis recorded on a ZrO2 crystal before and after Cs ion implantation at several ¯uences. Accumulation of damage in both the Zr and O sublattices of the ZrO2 crystal is evidenced by the decrease of the corresponding yields for the implanted samples, particularly strong at 5 1015 cm 2 (v0° Zr 0:7, v0° O 0:9 instead of 0.07 and 0.24, respectively, for the virgin crystal). Another remarkable feature is the reduced width of the O dips W1=2O 0:22° and 0.19° for the virgin and 5 1014 cm 2 implanted samples, respectively) as compared to the Zr dips (W1=2Zr 0:45° and 0.39°). Note also the shoulders present at 0.8° in the O dips of the virgin crystal, which are correlated to the special arrangement of the O atoms in the ZrO2 structure. The yield and width of the Cs dip measured on the sample implanted at a ¯uence of 5 1014 cm 2 (v0° Cs 0:30, W1=2Cs 0:30°) are reduced in comparison with the Zr dip. This result is likely due to the local atomic con®guration of Cs atoms. In ZrO2 the Zr atoms are located in the center of a cube formed by O atoms (ZrO8 dodecahedron), the distance between Zr and O atoms is 2.4 A, and the Zr atoms are in the Zr4 oxidation state [8]. Since the radius of Cs with a radius of 0.87 A [8], the atoms (in the Cs oxidation state) is 1.65 A substitution of a Zr atom by a Cs one should create a large stress in its vicinity. The stress relaxation certainly occurs via the formation of a Csvacancy complex surrounded by oxygen vacancies [9]. The fact that similar values of fS are obtained
for the various crystallographic orientations for this sample (see Table 1) indicates that Cs atoms are likely located isotropically around the center of ZrO8 dodecahedrons without any preferential orientation. Such an atomic con®guration would lead to the observed channeling eects. The increase of the Cs concentration leads to a strong decrease of the Cs yield v0° Cs 0:85 for the sample implanted at a ¯uence of 5 1015 cm 2 ). Such a decrease is correlated to a severe damage induced into the zirconia lattice by Cs ion implantation above a given ¯uence, demonstrated by the increase of the channeling yield exhibited in Figs. 1 (bump around channel 400) and 3(c) (v0° Zr 0:7, v0° O 0:9) and already observed for other implanted species [10±12]. An explanation of this loss of substitutionality could be the precipitation of implanted Cs atoms at high concentrations.
4. Conclusion The RBS/C data reported in this paper show a high substitutional fraction (more than 0.5) for Cs atoms implanted at low concentration (K0:5 at.%) into cubic ZrO2 single crystals. Angular scans across the main crystallographic axis indicate that such a value of the substitutional fraction is related to the formation of complexes with oxygen vacancies. Thus, the Cs atoms would be located near the center of ZrO8 cubes. On the contrary, when the Cs concentration is increased above 2±3 at.%, a strong disorder appears at the implantation depth in the host lattice, and the aligned yield measured on Cs is not far from the random yield. This ``randomization'' of the Cs lattice location could well be correlated to the precipitation of implanted species at high ¯uences. Transmission electron microscopy experiments are in progress to check this possibility.
Acknowledgements We want to thank the sta of the SEMIRAMIS group in the CSNSM-Orsay for ecient assistance during implantation and RBS experiments. This
L. Thome et al. / Nucl. Instr. and Meth. in Phys. Res. B 175±177 (2001) 453±457
work was partly supported by NATO under Linkage Grant no. PST/CLG 974800. References [1] Proceedings of the International Workshop on Advanced Reactors with Innovative Fuels, OECD Publications, Paris, 1999. [2] C. Degueldre, J.M. Paratte, Nucl. Technol. 123 (1998) 21. [3] C. Degueldre, J.M. Paratte, J. Nucl. Mater. 274 (1999) 1. [4] J. Chaumont, F. Lalu, M. Salome, A.M. Lamoise, H. Bernas, Nucl. Instr. and Meth. 189 (1981) 193. [5] E. Cottereau, J. Camplan, J. Chaumont, R. Meunier, H. Bernas, Nucl. Instr. and Meth. B 45 (1990) 293.
457
[6] J.F. Ziegler, J.P. Biersack, U. Littmark, in: J.F. Ziegler (Ed.), The Stopping and Range of Ions in Solids, Vol. 1, Pergamon, New York, 1985. [7] L.C. Feldman, J.W. Mayer, S.T. Picraux, in: Materials Analysis by Ion Channeling, Academic Press, New York, 1982, Chapter 5. [8] J. Emsley (Ed.), The Elements, Oxford University Press, Oxford, 1998. [9] A. Turos, Hj. Matzke, A. Drigo, A. Sambo, R. Falcone, Nucl. Instr. and Meth. B 113 (1996) 261. [10] D.Z. Xie, D.Z. Zhu, D.X. Cao, Z.Y. Zhou, Nucl. Instr. and Meth. B 132 (1997) 425. [11] K. Yasuda, M. Nastasi, K.E. Sickafus, C.J. Maggiore, N. Yu, Nucl. Instr. and Meth. B 136±138 (1998) 499. [12] K.E. Sickafus, Hj. Matzke, Th. Hartmann, K. Yasuda, J.A. Valdez, P. Chodak III, M. Nastasi, R.A. Verrall, J. Nucl. Mater. 274 (1999) 66.
www.elsevier.nl/locate/nimb
Lattice location of Cs atoms in cubic ZrO2 single crystals L. Thome a
a,*
, J. Jagielski
b,c
, A. Gentils a, F. Garrido
a
Centre de Spectrom etrie Nucl eaire et de Spectrom etrie de Masse, IN2P3-CNRS, B^ at. 108, 91405 Orsay, France b Institute of Electronic Materials Technology, Wolczynska 133, 01-919 Warsaw, Poland c The Andrzej Soltan Institute of Nuclear Studies, 05-400 Swierk/Otwock, Poland
Abstract The lattice location of a speci®c ®ssion product (Cs) implanted into cubic zirconia single crystals was investigated as a function of the atomic concentration by using Rutherford backscattering and channeling (RBS/C) experiments. At low concentration (<0.5 at.%), a signi®cant Cs substitutional fraction (0.5±0.6) is measured in channeling spectra recorded with the analyzing He beam aligned along the three main axes of the cubic crystal. Angular scans performed across the h1 0 0i axis indicate the formation of Cs-vacancy complexes. The ZrO2 single crystals are strongly damaged when the Cs concentration exceeds a few at.% and the Cs atoms are randomly located in the crystalline lattice. This latter result could be due to the precipitation of implanted Cs atoms. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 61.70.Vn; 61.80.Jh; 61.80.Mk Keywords: Doping and impurity implantation; Ion radiation eects; Channeling
1. Introduction Zirconium oxide (ZrO2 ) is a promising candidate as an inert matrix for the incineration of actinides originating from light-water reactors or dismounted nuclear weapons [1±3]. 1 Radiological-protection safety considerations lead to the study of the retention behaviour of radiotoxic isotopes (mostly ®ssion products) created in the material by nuclear reactions. Since the mobility of foreign species in a crystalline solid often depends *
Corresponding author. E-mail address: [email protected] (L. Thome). 1 For a review, see [1].
on their site in the host lattice, study of ®ssionproduct migration should include assessment of lattice location data. The present studies address such an issue. They rely on the determination by Rutherford backscattering and channeling (RBS/ C) experiments of the lattice sites of a speci®c ®ssion product (Cs) introduced in cubic ZrO2 single crystals by ion implantation. The in¯uence of several parameters, such as the radiation damage production and the ®ssion-product concentration, are also investigated. Besides their implications in the ®eld of nuclear waste management, the experiments reported in this paper deal with a more fundamental topic, namely the interaction between implanted ions and radiation defects.
0168-583X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 0 ) 0 0 5 3 4 - 6
454
L. Thome et al. / Nucl. Instr. and Meth. in Phys. Res. B 175±177 (2001) 453±457
2. Experimental The samples used are cubic {1 0 0}-oriented ZrO2 single crystals stabilized with 9:5 mol% Y2 O3 . They were implanted at room temperature with 300 keV 133 Cs2 ions delivered by the IRMA implanter [4] of the CSNSM in Orsay. The maximum ion ¯uence was 1016 cm 2 , which led to Cs concentrations up to 3 at.% in the implanted layer. A current density lower than 1 lA cm 2 was used in order to prevent excessive target heating. The damage created in the crystalline lattice and the lattice site of implanted ions was determined by RBS/C experiments with a 3.06 MeV 4 He2 ion beam provided by the ARAMIS accelerator [5] of the CSNSM. This energy was chosen in order to take advantage of the resonant elastic scattering on 16 O at 3.045 MeV. A standard acquisition set-up with an energy resolution of about 10 keV was used. Prior to
the RBS analysis the samples were covered with a 10 nm-thick carbon layer to avoid sample charging. 3. Results and discussion Typical RBS/C spectra recorded on ZrO2 single crystals implanted with various ¯uences of Cs ions are presented in Fig. 1. The spectrum recorded in a random direction displays the Zr edge (channel 410), the O signal enhanced by the resonance (channel 160) and a tiny Cs peak (channel 425). The spectrum recorded on a virgin sample in the h1 0 0i axial direction exhibits a strong decrease of the RBS yield due to the channeling eect vmin 0:05. The h1 0 0i axial yield increases with increasing ion ¯uences, more particularly at the implantation depth (channel 400), due to the damage created by Cs ion implantation. The inset of Fig. 1 shows a zoom on the Cs peaks (after careful background subtraction)
Fig. 1. Random (full symbols) and h1 0 0i-aligned (open symbols) RBS spectra recorded on cubic ZrO2 single crystals implanted with various ¯uences of Cs ions. Squares: before implantation; circles: 5 1014 cm 2 ; triangles: 5 1015 cm 2 . The inset presents a zoom on the Cs peak (¯uence: 5 1014 cm 2 ).
L. Thome et al. / Nucl. Instr. and Meth. in Phys. Res. B 175±177 (2001) 453±457
for spectra recorded in h1 0 0i axial and random directions on the sample implanted at a ¯uence of 5 1014 cm 2 . These peaks were reproduced with Gaussian distributions; the values of the mean projected ranges and range stragglings extracted from the ®ts to the data are in agreement with those calculated with the TRIM Monte-Carlo simulation code [6]. A strong decrease of the peak area is observed in the case where the analyzing beam is aligned along the h1 0 0i axial direction, indicating that Cs atoms are partly shadowed by host atoms along this direction. An estimation of the fraction of Cs ions located in a substitutional position (with respect to the h1 0 0i axis), fS , can be obtained from the analysis of the Cs peaks in RBS/C spectra. The values of fS , taken as (1 vi ) (where vi is the channeling yield measured on the Cs peaks), are represented in Fig. 2 as a function of the Cs concentration (at the peak maximum). It is worth noting that formally (1 vi ) should be normalized by (1 vh ) in order to derive the actual substitutional fraction (vh is the channeling yield obtained on the Zr host at the implantation depth) [7]. However, this normalization which is valid for relatively small values of vh leads to unrealistic substitutional fractions (often higher than 1) in the case of a strongly disordered crystal. At low atomic concentration (i.e. for an implantation ¯uence of 5 1014 cm 2 ), fS is about
Fig. 2. Substitutional fraction for Cs ions implanted into cubic ZrO2 single crystals as a function of the Cs concentration.
455
0.5 and the correction to account for the disorder in the host matrix would lead to a value of 0.6. Fig. 2 shows that the value of fS decreases as the Cs concentration increases and reaches zero at about 3 at.%. Table 1 Substitutional fraction (fS ) measured along the three main axes for Cs ions implanted at a ¯uence of 5 1014 cm 2 into a cubic ZrO2 single crystal Axis
fS
h1 0 0i h1 1 0i h1 1 1i
0:53 0:07 0:55 0:07 0:60 0:07
Fig. 3. Angular scans across the h1 0 0i axis for Zr (®lled circles), O (open circles) and Cs (dotted triangles): (a) virgin crystal; (b) crystal implanted with 5 1014 cm 2 ; (c) crystal implanted with 5 1015 cm 2 .
456
L. Thome et al. / Nucl. Instr. and Meth. in Phys. Res. B 175±177 (2001) 453±457
The fraction of Cs atoms in fully substitutional sites (i.e. with respect to the various crystallographic orientations) can only be obtained by measuring the values of fS along the three main axial directions of the cubic ZrO2 lattice. Such values (not corrected by the host dechanneling) are reported in Table 1 for the sample implanted at low Cs concentration (¯uence: 5 1014 cm 2 ). The results show that the values of fS obtained along the three main axes lie in the range 0.5±0.6. This result con®rms that the actual fraction of Cs atoms lying in substitutional sites is around 60%. Additional information concerning the lattice location of implanted ions can be obtained by measuring the angular dependence of the backscattering yield through low-index axes. Fig. 3 presents angular scans across the h1 0 0i axis recorded on a ZrO2 crystal before and after Cs ion implantation at several ¯uences. Accumulation of damage in both the Zr and O sublattices of the ZrO2 crystal is evidenced by the decrease of the corresponding yields for the implanted samples, particularly strong at 5 1015 cm 2 (v0° Zr 0:7, v0° O 0:9 instead of 0.07 and 0.24, respectively, for the virgin crystal). Another remarkable feature is the reduced width of the O dips W1=2O 0:22° and 0.19° for the virgin and 5 1014 cm 2 implanted samples, respectively) as compared to the Zr dips (W1=2Zr 0:45° and 0.39°). Note also the shoulders present at 0.8° in the O dips of the virgin crystal, which are correlated to the special arrangement of the O atoms in the ZrO2 structure. The yield and width of the Cs dip measured on the sample implanted at a ¯uence of 5 1014 cm 2 (v0° Cs 0:30, W1=2Cs 0:30°) are reduced in comparison with the Zr dip. This result is likely due to the local atomic con®guration of Cs atoms. In ZrO2 the Zr atoms are located in the center of a cube formed by O atoms (ZrO8 dodecahedron), the distance between Zr and O atoms is 2.4 A, and the Zr atoms are in the Zr4 oxidation state [8]. Since the radius of Cs with a radius of 0.87 A [8], the atoms (in the Cs oxidation state) is 1.65 A substitution of a Zr atom by a Cs one should create a large stress in its vicinity. The stress relaxation certainly occurs via the formation of a Csvacancy complex surrounded by oxygen vacancies [9]. The fact that similar values of fS are obtained
for the various crystallographic orientations for this sample (see Table 1) indicates that Cs atoms are likely located isotropically around the center of ZrO8 dodecahedrons without any preferential orientation. Such an atomic con®guration would lead to the observed channeling eects. The increase of the Cs concentration leads to a strong decrease of the Cs yield v0° Cs 0:85 for the sample implanted at a ¯uence of 5 1015 cm 2 ). Such a decrease is correlated to a severe damage induced into the zirconia lattice by Cs ion implantation above a given ¯uence, demonstrated by the increase of the channeling yield exhibited in Figs. 1 (bump around channel 400) and 3(c) (v0° Zr 0:7, v0° O 0:9) and already observed for other implanted species [10±12]. An explanation of this loss of substitutionality could be the precipitation of implanted Cs atoms at high concentrations.
4. Conclusion The RBS/C data reported in this paper show a high substitutional fraction (more than 0.5) for Cs atoms implanted at low concentration (K0:5 at.%) into cubic ZrO2 single crystals. Angular scans across the main crystallographic axis indicate that such a value of the substitutional fraction is related to the formation of complexes with oxygen vacancies. Thus, the Cs atoms would be located near the center of ZrO8 cubes. On the contrary, when the Cs concentration is increased above 2±3 at.%, a strong disorder appears at the implantation depth in the host lattice, and the aligned yield measured on Cs is not far from the random yield. This ``randomization'' of the Cs lattice location could well be correlated to the precipitation of implanted species at high ¯uences. Transmission electron microscopy experiments are in progress to check this possibility.
Acknowledgements We want to thank the sta of the SEMIRAMIS group in the CSNSM-Orsay for ecient assistance during implantation and RBS experiments. This
L. Thome et al. / Nucl. Instr. and Meth. in Phys. Res. B 175±177 (2001) 453±457
work was partly supported by NATO under Linkage Grant no. PST/CLG 974800. References [1] Proceedings of the International Workshop on Advanced Reactors with Innovative Fuels, OECD Publications, Paris, 1999. [2] C. Degueldre, J.M. Paratte, Nucl. Technol. 123 (1998) 21. [3] C. Degueldre, J.M. Paratte, J. Nucl. Mater. 274 (1999) 1. [4] J. Chaumont, F. Lalu, M. Salome, A.M. Lamoise, H. Bernas, Nucl. Instr. and Meth. 189 (1981) 193. [5] E. Cottereau, J. Camplan, J. Chaumont, R. Meunier, H. Bernas, Nucl. Instr. and Meth. B 45 (1990) 293.
457
[6] J.F. Ziegler, J.P. Biersack, U. Littmark, in: J.F. Ziegler (Ed.), The Stopping and Range of Ions in Solids, Vol. 1, Pergamon, New York, 1985. [7] L.C. Feldman, J.W. Mayer, S.T. Picraux, in: Materials Analysis by Ion Channeling, Academic Press, New York, 1982, Chapter 5. [8] J. Emsley (Ed.), The Elements, Oxford University Press, Oxford, 1998. [9] A. Turos, Hj. Matzke, A. Drigo, A. Sambo, R. Falcone, Nucl. Instr. and Meth. B 113 (1996) 261. [10] D.Z. Xie, D.Z. Zhu, D.X. Cao, Z.Y. Zhou, Nucl. Instr. and Meth. B 132 (1997) 425. [11] K. Yasuda, M. Nastasi, K.E. Sickafus, C.J. Maggiore, N. Yu, Nucl. Instr. and Meth. B 136±138 (1998) 499. [12] K.E. Sickafus, Hj. Matzke, Th. Hartmann, K. Yasuda, J.A. Valdez, P. Chodak III, M. Nastasi, R.A. Verrall, J. Nucl. Mater. 274 (1999) 66.