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Doppler broadening measurements of positron annihilation using bremsstrahlung radiation
Nuclear Instruments and Methods in Physics Research B 192 (2002) 197–201 www.elsevier.com/locate/nimb
Doppler broadening measurements of positron annihilation using bremsstrahlung radiation F.A. Selim a,*, D.P. Wells a, J.F. Harmon a, W. Scates a, J. Kwofie a, R. Spaulding a, S.P. Duttagupta b, J.L. Jones c, T. White c, T. Roney c a
Department of Physics, Idaho Accelerator Center, Idaho State University, Campus Box 8263, Pocatello, ID 83209, USA b Department of Electrical Engineering, Boise State University, Campus Box 2075, ID 83725, USA c Idaho National Engineering and Environmental Laboratory, P.O. Box 1625-2802, Idaho Falls, ID 83415, USA
Abstract The first system to measure Doppler broadening of positron annihilation based on during electron-pulse bremsstrahlung radiation has been constructed and demonstrated. No photon-induced activation or positron emitters are involved in the process. The collimated bremsstrahlung radiation from a small electron accelerator, which exhibits excellent penetrability, is used to generate positrons inside the sample via pair production. The annihilation photons are recorded by a HPGe detector. The line-shape parameters of Doppler broadening can be used to identify defects in pure metals and alloys. The dependence of these parameters on different elements has been measured and shows promise as a probe of momentum of electronic wave-functions in pure and composite materials. This method also shows promise as an additional tool for measuring elemental composition, when used in conjunction with accelerator-based X-ray fluorescence. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 78.70.Bj; 41.75.Fr Keywords: Bremsstrahlung; Positron annihilation; Doppler broadening; Defect measurements
1. Introduction Positron annihilation Doppler broadening spectroscopy is a well established tool to probe and characterize defects [1,2]. The 511 keV peak is Doppler broadened by the longitudinal momentum of the annihilating pairs. Since the positrons are thermalized, the Doppler broadening measurements provide information about the mo-
*
Corresponding author. Tel.: +208-282-5874; fax: +208-2825878. E-mail address: [email protected] (F.A. Selim).
mentum distributions of electrons at the annihilation site. Two parameters S (for shape), and W (for wings) see e.g. [3,4] are usually used to characterize the annihilation peak. The S parameter is more sensitive to the annihilation with low momentum valence and unbound electrons and is defined as the ratio of the counts in the central region of the peak to the total counts in the peak. The W parameter is more sensitive to the annihilation with high momentum core electrons and is defined as the ratio of counts in the wing regions of the peak to the total counts in the peak. A high concentration of defects, or an increase in the mean size of defects, leads to a larger contribution
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 0 8 6 8 - 6
198
F.A. Selim et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 197–201
of annihilation photons from low momentum electrons because positrons are trapped at defects see e.g. [5,6]. This is reflected in Doppler broadening measurements by an increase in S parameter and a decrease in W parameter. Essentially all prior Doppler broadening measurements see e.g. [3–9] have been performed using either slow positron beams or wide-energy-spectrum positron beams from radioactive sources. The thickness of the samples under investigation by these methods is severely limited by the range of the impinging positrons inside the sample. Typical target thicknesses range from lg/cm2 to mg/cm2 . In addition, the high cost and complexities of obtaining positron beams has limited the application of Doppler broadening spectroscopy techniques to basic materials science with little commercial or industrial application. We report here the first measurements of positron annihilation Doppler broadening based on bremsstrahlung radiation. The collimated bremsstrahlung beam from a small electron accelerator (6 MeV Linac) is used to generate positrons inside the sample through pair production. No photoninduced activation is involved in the process. The annihilation photons are recorded during the pulse by a high energy resolution HPGe detector. The Doppler broadened spectra of the 511 keV annihilation photons are analyzed in terms of S parameter. The high penetrability of bremsstrahlung photons allows one to study defects in thick samples up to tens of g/cm2 , a thickness that is inaccessible by conventional positron beam techniques. This technique also provides a relatively inexpensive method for measuring Doppler broadening. These advantages open the door to exploit positron annihilation spectroscopy for a variety of commercial and industrial applications, as well as a new tool for materials science. An additional utility to these measurements stems from the sensitivity of yield and S parameter to the chemical environment of the sample. We studied the dependence of S parameter on atomic number, with the purpose of combining Doppler broadening measurements with X-ray fluorescence (XRF) to gain a more complete assay for samples under analysis.
2. Experimental set-up and sample preparation We use a pulsed 6 MeV electron beam that is incident upon a thick tungsten converter. These pulses are at order of 2 ls with a repetition rate of 200 Hz. The resulting bremsstrahlung photons are doubly collimated with a 20 cm thick, 0.6 cm diameter stainless steel primary collimator, followed by a 15 cm thick, 1.8 cm diameter lead secondary collimator two meters downstream (see Fig. 1). This photon beam is incident upon the sample, resulting in pair production throughout the volume of the sample, as well as other electromagnetic processes that produce background such as Compton scattering and the photo-electric effect. One or more HPGe detectors are typically placed at 90° to maximize solid angle and used to record the spectrum. These detectors are shielded with at least 10 cm of lead. Their field-of-view is restricted with a 2.54 cm diameter lead collimator and we typically employ 5–10 cm of aluminum to reduce
Fig. 1. A schematic of the experimental set-up showing the LINAC, beam collimation, target position, detector orientation, and detector shielding and collimation.
F.A. Selim et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 197–201
the low energy characteristic X-rays from the target. Fig. 1 shows greater detail of the experiment set-up. Signals from the detectors are pre-amplified and sent to a spectroscopy amplifier, and then sent to an ADC. The energy resolution of these detectors varied from 1.2 to 1.6 keV at the 133 Ba c-line of 356 keV. It should be noted that since we count during the pulse, our counting rate is limited by the fraction of time that the electron Linac is on (104 ). For the positron annihilation study of tensile stress, low carbon, low alloy 10–20 steel samples were used. All the samples were machined for standard engineering strain measurements. The cross-sectional area of the neck of the samples was 0.64 cm by 1.0 cm. The samples were annealed at 871 °C for 2 h before exposed to stress. Different tensile loads were applied to the samples to obtain strain ranging from 0% to 32% of the original length of the neck. For the Doppler broadening measurements of elemental analysis, we used high purity materials (>99.99% purity) of Ti, Cu, Sn and Pb. Since Pb and Sn are self annealing materials, we only annealed Cu and Ti before the Doppler broadening measurements.
199
Fig. 2. A representative spectrum of in-beam positron annihilation yield. The lead XRF peaks at approximately 75 keV, the large and broad Compton yield at approximately 270 keV, and the 40 K yield at 1460 keV can also be seen.
3. Results and discussion The entire spectrum emitted from the target and recorded by the HPGe detector is shown in Fig. 2. The background with the bremsstrahlung beam, but without a target, has been measured and found to be negligible. The yield of 511 keV photons in background measurements is less than 1% of the yield with a target in the beam. Background associated with electromagnetic processes in the target (shown in Fig. 2) is primarily due to the Thomson/Compton scattering of bremsstrahlung photons from electrons in the target, with an additional background from photo-electric effect induced XRF in the target. The S parameter is obtained by dividing the counts in the central zone of the 511 keV peak to the total counts in the peak, after subtracting background. For the steel samples, the measurements have been performed three times under differing experimental conditions with different
Fig. 3. The relative S parameter versus strain. Note that the steel sample represented by the last point on the curve was stressed beyond the breaking point.
detectors and with different energy resolutions. Figs. 3 and 4 show the plots of the combined results of these three measurements. The relative S as a function of strain in the steel is plotted in Fig. 3, where relative S is defined as the sample S divided by Sreference (the unstressed sample). Fig. 4 shows the same relative S as a function of stress. Note that the last point on both curves represent the relative S parameter for a sample that was stressed beyond the breaking point (stress ¼ 44 642 N/cm2 ), while the next closest point on the
200
F.A. Selim et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 197–201
Fig. 4. The relative S versus stress. These data are the same as in Fig. 3. Note that the steel sample represented by the last point on the curve was stressed beyond the breaking point.
curve is just below the breaking point (stress ¼ 44 503 N/cm2 ). It is extremely interesting to note that the relative S parameter increases smoothly, monotonically and (apparently) linearly with strain to very near the breaking point of the steel; however, much of the increase in S, and the increase in strain, occurs over a relatively narrow range of stress. It remains to be seen what the shape of the curve is over the narrow range of stress between these two points or, equivalently, between the strains of 0.16 and 0.32. Uncertainties are dominated by counting statistics. These errors are large because of the low repetition rate of these beams. Systematic errors however tend to cancel because we are taking ratios to estimate relative S. The dependence of the S parameter upon atomic number is shown in Fig. 5. We find a general trend of increasing S value for increasing atomic number; however, the uncertainties in these measurements, and the fact that only four elements were measured, makes it difficult to draw strong conclusions about the dependence of S upon atomic number. While we know of no general theory that predicts the value of S as a function of atomic number, Alatalo et al. [10] predict a general increasing trend of S as one goes vertically down (increasing Z) the columns of the periodic table, and as one goes horizontally across the rows of
Fig. 5. The S parameter versus atomic number.
the periodic table (increasing Z). Our data do not show these trends, although the large uncertainties in these data do not permit a definitive statement of consistency, or lack thereof. To reduce the background arising from the scattering of bremsstrahlung photons inside the target, and to greatly increase counting rates, we are in the process of replacing the pulsed bremsstrahlung beam with a continuous wattage (CW) bremsstrahlung beam, and detecting the 511 photons using coincidence techniques. The CW beam will improve the single-detector counting rate by approximately 104 , and will allow us to do coincidence measurements to resolve the highest momentum parts of the 511 keV peak.
4. Conclusions Our most important result is that we have demonstrated the feasibility of a new technique to measure Doppler broadening of 511 keV annihilation photons. This technique employs in-beam measurements of annihilation photons from bremsstrahlung-induced pair-production. The primary advantages of this technique over conventional methods that employ sources or positron beams is that the high penetrability of bremsstrahlung photons allows measurements of strain or defects for very thick targets, up to several tens
F.A. Selim et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 197–201
of g/cm2 . Further, the portability, reliability and relatively low cost of low-energy electron linacs suggests that this technique could be widely exploited in commercial or industrial applications. This technique could potentially also be used for dynamic measurements of strain where, for example, the strain of turbine components could be measured while the turbine is rotating. The most obvious limitations of this technique are (i) the relatively high Compton and XRF backgrounds induced from the bremsstrahlung beam and (ii) the relatively low counting rate associated with pulsed beams. The latter can be addressed with CW electron beams, at the cost of portability or beams of higher repetition rate. Background reduction can be achieved via coincidence techniques, at the cost of counting rate; however, for single-detector setups the background is a fundamental limitation that one cannot avoid. Acknowledgements This work has been supported by Inland Northwest Research Alliance under contract ISU001
201
and Bechtel BXXT ID, LLC under contract M2nT041nC95-175697. References [1] P. Hautojarvi, A. Vehanen, in: P. Hautojarvi (Ed.), Positrons in Solids, 1979, p. 1. [2] A. Dupasquier, A.P. Mills (Eds.), Positron Spectroscopy of Solids, 1995. [3] P. Asoka-Kumar, K.G. Lynn, D.O. Welch, J. Appl. Phys. 76 (1994) 4935. [4] J.M. Urban-Klaehen, C.A. Quarles, J. Appl. Phys. 86 (1999) 355. [5] P.J. Schultz, K.G. Lynn, Rev. Mod. Phys. 60 (1988) 701. [6] A. Osipowicz, M. Harting, M. Hempel, D.T. Britton, W. Bauer-Kugelmann, W. Triftshauser, Appl. Surf. Sci. 149 (1999) 198. [7] V. Thaveeprungsriporn, P. Swatewaacharkul, K. Talerngsuk, S. Punnachaiya, D. Thong-Aram, Nucl. Instr. and Meth. B 155 (1999) 459. [8] R. Escobar Galindo, A. Van Veen, A. Alba Garcia, H. Schut, J.Th. De Hosson, in: Proceedings of the Twelfth Conference on Positron Annihilation, 2000, p. 499. [9] F. Hori, R. Oshima, in: Proceedings of the Twelfth Conference on Positron Annihilation, 2000, p. 204. [10] M. Alatalo, B. Barbiellini, M. Hakala, H. Kauppinem, T. Korhonen, M.J. Puska, K. Saarinen, P. Hautokjarvi, R.M. Nieminen, Phy. Rev. B 54 (1996) 2397.
Doppler broadening measurements of positron annihilation using bremsstrahlung radiation F.A. Selim a,*, D.P. Wells a, J.F. Harmon a, W. Scates a, J. Kwofie a, R. Spaulding a, S.P. Duttagupta b, J.L. Jones c, T. White c, T. Roney c a
Department of Physics, Idaho Accelerator Center, Idaho State University, Campus Box 8263, Pocatello, ID 83209, USA b Department of Electrical Engineering, Boise State University, Campus Box 2075, ID 83725, USA c Idaho National Engineering and Environmental Laboratory, P.O. Box 1625-2802, Idaho Falls, ID 83415, USA
Abstract The first system to measure Doppler broadening of positron annihilation based on during electron-pulse bremsstrahlung radiation has been constructed and demonstrated. No photon-induced activation or positron emitters are involved in the process. The collimated bremsstrahlung radiation from a small electron accelerator, which exhibits excellent penetrability, is used to generate positrons inside the sample via pair production. The annihilation photons are recorded by a HPGe detector. The line-shape parameters of Doppler broadening can be used to identify defects in pure metals and alloys. The dependence of these parameters on different elements has been measured and shows promise as a probe of momentum of electronic wave-functions in pure and composite materials. This method also shows promise as an additional tool for measuring elemental composition, when used in conjunction with accelerator-based X-ray fluorescence. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 78.70.Bj; 41.75.Fr Keywords: Bremsstrahlung; Positron annihilation; Doppler broadening; Defect measurements
1. Introduction Positron annihilation Doppler broadening spectroscopy is a well established tool to probe and characterize defects [1,2]. The 511 keV peak is Doppler broadened by the longitudinal momentum of the annihilating pairs. Since the positrons are thermalized, the Doppler broadening measurements provide information about the mo-
*
Corresponding author. Tel.: +208-282-5874; fax: +208-2825878. E-mail address: [email protected] (F.A. Selim).
mentum distributions of electrons at the annihilation site. Two parameters S (for shape), and W (for wings) see e.g. [3,4] are usually used to characterize the annihilation peak. The S parameter is more sensitive to the annihilation with low momentum valence and unbound electrons and is defined as the ratio of the counts in the central region of the peak to the total counts in the peak. The W parameter is more sensitive to the annihilation with high momentum core electrons and is defined as the ratio of counts in the wing regions of the peak to the total counts in the peak. A high concentration of defects, or an increase in the mean size of defects, leads to a larger contribution
0168-583X/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 5 8 3 X ( 0 2 ) 0 0 8 6 8 - 6
198
F.A. Selim et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 197–201
of annihilation photons from low momentum electrons because positrons are trapped at defects see e.g. [5,6]. This is reflected in Doppler broadening measurements by an increase in S parameter and a decrease in W parameter. Essentially all prior Doppler broadening measurements see e.g. [3–9] have been performed using either slow positron beams or wide-energy-spectrum positron beams from radioactive sources. The thickness of the samples under investigation by these methods is severely limited by the range of the impinging positrons inside the sample. Typical target thicknesses range from lg/cm2 to mg/cm2 . In addition, the high cost and complexities of obtaining positron beams has limited the application of Doppler broadening spectroscopy techniques to basic materials science with little commercial or industrial application. We report here the first measurements of positron annihilation Doppler broadening based on bremsstrahlung radiation. The collimated bremsstrahlung beam from a small electron accelerator (6 MeV Linac) is used to generate positrons inside the sample through pair production. No photoninduced activation is involved in the process. The annihilation photons are recorded during the pulse by a high energy resolution HPGe detector. The Doppler broadened spectra of the 511 keV annihilation photons are analyzed in terms of S parameter. The high penetrability of bremsstrahlung photons allows one to study defects in thick samples up to tens of g/cm2 , a thickness that is inaccessible by conventional positron beam techniques. This technique also provides a relatively inexpensive method for measuring Doppler broadening. These advantages open the door to exploit positron annihilation spectroscopy for a variety of commercial and industrial applications, as well as a new tool for materials science. An additional utility to these measurements stems from the sensitivity of yield and S parameter to the chemical environment of the sample. We studied the dependence of S parameter on atomic number, with the purpose of combining Doppler broadening measurements with X-ray fluorescence (XRF) to gain a more complete assay for samples under analysis.
2. Experimental set-up and sample preparation We use a pulsed 6 MeV electron beam that is incident upon a thick tungsten converter. These pulses are at order of 2 ls with a repetition rate of 200 Hz. The resulting bremsstrahlung photons are doubly collimated with a 20 cm thick, 0.6 cm diameter stainless steel primary collimator, followed by a 15 cm thick, 1.8 cm diameter lead secondary collimator two meters downstream (see Fig. 1). This photon beam is incident upon the sample, resulting in pair production throughout the volume of the sample, as well as other electromagnetic processes that produce background such as Compton scattering and the photo-electric effect. One or more HPGe detectors are typically placed at 90° to maximize solid angle and used to record the spectrum. These detectors are shielded with at least 10 cm of lead. Their field-of-view is restricted with a 2.54 cm diameter lead collimator and we typically employ 5–10 cm of aluminum to reduce
Fig. 1. A schematic of the experimental set-up showing the LINAC, beam collimation, target position, detector orientation, and detector shielding and collimation.
F.A. Selim et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 197–201
the low energy characteristic X-rays from the target. Fig. 1 shows greater detail of the experiment set-up. Signals from the detectors are pre-amplified and sent to a spectroscopy amplifier, and then sent to an ADC. The energy resolution of these detectors varied from 1.2 to 1.6 keV at the 133 Ba c-line of 356 keV. It should be noted that since we count during the pulse, our counting rate is limited by the fraction of time that the electron Linac is on (104 ). For the positron annihilation study of tensile stress, low carbon, low alloy 10–20 steel samples were used. All the samples were machined for standard engineering strain measurements. The cross-sectional area of the neck of the samples was 0.64 cm by 1.0 cm. The samples were annealed at 871 °C for 2 h before exposed to stress. Different tensile loads were applied to the samples to obtain strain ranging from 0% to 32% of the original length of the neck. For the Doppler broadening measurements of elemental analysis, we used high purity materials (>99.99% purity) of Ti, Cu, Sn and Pb. Since Pb and Sn are self annealing materials, we only annealed Cu and Ti before the Doppler broadening measurements.
199
Fig. 2. A representative spectrum of in-beam positron annihilation yield. The lead XRF peaks at approximately 75 keV, the large and broad Compton yield at approximately 270 keV, and the 40 K yield at 1460 keV can also be seen.
3. Results and discussion The entire spectrum emitted from the target and recorded by the HPGe detector is shown in Fig. 2. The background with the bremsstrahlung beam, but without a target, has been measured and found to be negligible. The yield of 511 keV photons in background measurements is less than 1% of the yield with a target in the beam. Background associated with electromagnetic processes in the target (shown in Fig. 2) is primarily due to the Thomson/Compton scattering of bremsstrahlung photons from electrons in the target, with an additional background from photo-electric effect induced XRF in the target. The S parameter is obtained by dividing the counts in the central zone of the 511 keV peak to the total counts in the peak, after subtracting background. For the steel samples, the measurements have been performed three times under differing experimental conditions with different
Fig. 3. The relative S parameter versus strain. Note that the steel sample represented by the last point on the curve was stressed beyond the breaking point.
detectors and with different energy resolutions. Figs. 3 and 4 show the plots of the combined results of these three measurements. The relative S as a function of strain in the steel is plotted in Fig. 3, where relative S is defined as the sample S divided by Sreference (the unstressed sample). Fig. 4 shows the same relative S as a function of stress. Note that the last point on both curves represent the relative S parameter for a sample that was stressed beyond the breaking point (stress ¼ 44 642 N/cm2 ), while the next closest point on the
200
F.A. Selim et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 197–201
Fig. 4. The relative S versus stress. These data are the same as in Fig. 3. Note that the steel sample represented by the last point on the curve was stressed beyond the breaking point.
curve is just below the breaking point (stress ¼ 44 503 N/cm2 ). It is extremely interesting to note that the relative S parameter increases smoothly, monotonically and (apparently) linearly with strain to very near the breaking point of the steel; however, much of the increase in S, and the increase in strain, occurs over a relatively narrow range of stress. It remains to be seen what the shape of the curve is over the narrow range of stress between these two points or, equivalently, between the strains of 0.16 and 0.32. Uncertainties are dominated by counting statistics. These errors are large because of the low repetition rate of these beams. Systematic errors however tend to cancel because we are taking ratios to estimate relative S. The dependence of the S parameter upon atomic number is shown in Fig. 5. We find a general trend of increasing S value for increasing atomic number; however, the uncertainties in these measurements, and the fact that only four elements were measured, makes it difficult to draw strong conclusions about the dependence of S upon atomic number. While we know of no general theory that predicts the value of S as a function of atomic number, Alatalo et al. [10] predict a general increasing trend of S as one goes vertically down (increasing Z) the columns of the periodic table, and as one goes horizontally across the rows of
Fig. 5. The S parameter versus atomic number.
the periodic table (increasing Z). Our data do not show these trends, although the large uncertainties in these data do not permit a definitive statement of consistency, or lack thereof. To reduce the background arising from the scattering of bremsstrahlung photons inside the target, and to greatly increase counting rates, we are in the process of replacing the pulsed bremsstrahlung beam with a continuous wattage (CW) bremsstrahlung beam, and detecting the 511 photons using coincidence techniques. The CW beam will improve the single-detector counting rate by approximately 104 , and will allow us to do coincidence measurements to resolve the highest momentum parts of the 511 keV peak.
4. Conclusions Our most important result is that we have demonstrated the feasibility of a new technique to measure Doppler broadening of 511 keV annihilation photons. This technique employs in-beam measurements of annihilation photons from bremsstrahlung-induced pair-production. The primary advantages of this technique over conventional methods that employ sources or positron beams is that the high penetrability of bremsstrahlung photons allows measurements of strain or defects for very thick targets, up to several tens
F.A. Selim et al. / Nucl. Instr. and Meth. in Phys. Res. B 192 (2002) 197–201
of g/cm2 . Further, the portability, reliability and relatively low cost of low-energy electron linacs suggests that this technique could be widely exploited in commercial or industrial applications. This technique could potentially also be used for dynamic measurements of strain where, for example, the strain of turbine components could be measured while the turbine is rotating. The most obvious limitations of this technique are (i) the relatively high Compton and XRF backgrounds induced from the bremsstrahlung beam and (ii) the relatively low counting rate associated with pulsed beams. The latter can be addressed with CW electron beams, at the cost of portability or beams of higher repetition rate. Background reduction can be achieved via coincidence techniques, at the cost of counting rate; however, for single-detector setups the background is a fundamental limitation that one cannot avoid. Acknowledgements This work has been supported by Inland Northwest Research Alliance under contract ISU001
201
and Bechtel BXXT ID, LLC under contract M2nT041nC95-175697. References [1] P. Hautojarvi, A. Vehanen, in: P. Hautojarvi (Ed.), Positrons in Solids, 1979, p. 1. [2] A. Dupasquier, A.P. Mills (Eds.), Positron Spectroscopy of Solids, 1995. [3] P. Asoka-Kumar, K.G. Lynn, D.O. Welch, J. Appl. Phys. 76 (1994) 4935. [4] J.M. Urban-Klaehen, C.A. Quarles, J. Appl. Phys. 86 (1999) 355. [5] P.J. Schultz, K.G. Lynn, Rev. Mod. Phys. 60 (1988) 701. [6] A. Osipowicz, M. Harting, M. Hempel, D.T. Britton, W. Bauer-Kugelmann, W. Triftshauser, Appl. Surf. Sci. 149 (1999) 198. [7] V. Thaveeprungsriporn, P. Swatewaacharkul, K. Talerngsuk, S. Punnachaiya, D. Thong-Aram, Nucl. Instr. and Meth. B 155 (1999) 459. [8] R. Escobar Galindo, A. Van Veen, A. Alba Garcia, H. Schut, J.Th. De Hosson, in: Proceedings of the Twelfth Conference on Positron Annihilation, 2000, p. 499. [9] F. Hori, R. Oshima, in: Proceedings of the Twelfth Conference on Positron Annihilation, 2000, p. 204. [10] M. Alatalo, B. Barbiellini, M. Hakala, H. Kauppinem, T. Korhonen, M.J. Puska, K. Saarinen, P. Hautokjarvi, R.M. Nieminen, Phy. Rev. B 54 (1996) 2397.