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Spectroscopic investigations of smooth hydrocarbon deuterated erosion flakes deposited from tokamak T-10 deuterium plasma discharge
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 543 (2005) 225–228 www.elsevier.com/locate/nima
Spectroscopic investigations of smooth hydrocarbon deuterated erosion flakes deposited from tokamak T-10 deuterium plasma discharge N.Yu. Svechnikova, V.G. Stankevicha, A.M. Lebedeva,, K.A. Menshikova, B.N. Kolbasova, N.M. Kocherginskyb, D. Rajarathnamb, Yu. Kostetskib, S.N. Ivanovc, V.V. Kriventsovd a
Russian Research Center Kurchatov Institute, Moscow 123128, Russian Federation b Faculty of Engineering, National University of Singapore, Singapore c Physical Faculty, Moscow State University, Moscow, Russian Federation d Boreskov Institute of Catalysis, Novosibirsk 630090, Russian Federation Available online 5 March 2005
Abstract Investigations of smooth deuterated carbon erosion films co-deposited from deuterium plasma discharges inside the tokamak T-10 vacuum chamber were carried out using UV–VIS and X-ray photoluminescence, UV reflection, EXAFS, EPR, and temperature measurements. The influence of defective states on photoluminescence and its temperature quenching are discussed. r 2005 Elsevier B.V. All rights reserved. PACS: 78.55.m; 78.66.Tr; 73.61.Ph; 52.55.Pi Keywords: Luminescence; Reflection; a-C:H; EPR; EXAFS; Vibration modes
1. Introduction The operational safety of the International Thermonuclear Experimental Reactor (ITER) may be seriously affected by the erosion of Corresponding author. Tel.: +7 095 1969017;
fax: +7 095 1967538. E-mail address: [email protected] (A.M. Lebedev).
plasma-facing materials, resulting in the formation of smooth hydrogenated carbon films (‘‘flakes’’) codeposited from plasma discharges inside the vacuum chamber. Such films can accumulate large amounts of hydrogen isotopes H, D, T (radioactive), and require a difficult cleaning procedure of the walls, mechanical or thermal. Therefore, it is necessary to know the electronic structure of such new systems, which has not been studied earlier,
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.187
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and it is also necessary to control the amounts of H-isotopes, since these strongly influence the electronic structure. The samples were smooth carbon erosion films with a high hydrogen isotope concentration (D/C0.5, H/C0.3), produced from D-plasma discharge of the tokamak T-10 operating in the RRC Kurchatov Institute [1]. The erosion films possess cracks and other defects causing their flaking and separation from the walls. The films are very brittle, concave shaped from the plasma side, with a 10 mm thickness and a 0.5 cm2 size. The analogous systems (but more simple) are known as amorphous a-C:H and a-C:D carbon films [2,3]. Their valence band structure is determined by a mixture of mainly sp3 (diamond-like) and sp2 (graphite-like) states, and this can be changed due to heating or defect formation. The sp2 clusters are known to form s and s extended states, and p-states localized inside a s–s gap, while sp2 clusters are imbedded in a dielectric sp3 matrix. For photon energies up to 6–8 eV, the absorption of light is described in terms of p–p transitions, and photoluminescence is attributed to electron–hole (e–h) recombination in the p-localized states of sp2 clusters. The defect states are identified within the band gap, and these control non-radiative recombination.
2. Experiments and discussion The photoluminescence spectra were taken at room temperature for the annealed samples at 200 and 450 1C, employing a PTI Instruments’ Quantamaster QM-5 Fluorescence system equipped with a pulsed xenon lamp source and a PMT detector. The normalized emission and luminescence excitation spectra are shown in Fig. 1 for 200 1C (as known for a-C:H films, annealing to T ¼ 1002200 1C may lead to some growth of luminescence intensity, due to H-saturation of carbon dangling bonds serving as non-radiative recombination centers [3]). The emission (under 372 nm excitation) is occupying the interval 390–600 nm (3.18–2.1 eV), and this has a certain structure with a maximum at 450 nm, and an FWHM ¼ 70 nm: Almost a mirror-like lumines-
Fig. 1. Normalized emission and luminescence excitation spectra of the tokamak film annealed to 200 1C.
cence excitation spectrum, taken under luminescence observation at 450 nm (2.76 eV), is occupying the interval 230–450 nm (5.4–2.8 eV) with a maximum near 370 nm (3.35 eV). These data indicate a gap value Eg3 eV. The Stokes shift is equal to 3.352.76 ¼ 0.59 eV. This rather weak overlapping of emission and excitation spectra, together with a noticeable Stokes shift ð0:59 eVbkT 0:025 eVÞ; point to a certain possibility for non-radiative recombination [4]. In principle, these spectra can be deconvoluted to 3–4 Gaussians. Similar spectra are typical of excitonic luminescence for a-C:H films [3]. A rather small bandwidth can be referred to a rather strong localization of photogenerated e–h pairs inside an sp2 cluster [5]. Photoluminescence was found to be almost quenched (to the background level) after baking to 450 1C in a nitrogen atmosphere, due to non-radiative energy dissipation caused, probably, by disordered sp2 aromatic network. In Fig. 2, the normalized luminescence excitation spectra of tokamak flakes and C60 thin films are shown. The measurements were performed at the Universal VUV spectrometer D’4.2 of the Siberia-1 SR source in the range of 3–10 eV at 300 K. Photoluminescence was registered with a FEU-100 PMT (maximum sensitivity near 420 nm). The excitation spectrum (dash-dot line) from Fig. 1, normalized to the first peak of the C60 curve is shown for comparison. This picture shows
ARTICLE IN PRESS N.Yu. Svechnikov et al. / Nuclear Instruments and Methods in Physics Research A 543 (2005) 225–228
___ __exper. _ _ _ theory
4.00 6.00 8.00 10.00 Wave number (Å-1)
Magnitude of FT (a.u.)
a definite similarity between excitation spectra of erosion films and those for C60. The tokamak peaks at 3.34, 5.47, 6.5 and 8.36 eV are close to the position of C60 peaks, and the latter refers to C2p p-states and to p þ s mixed states for C QC aromatic rings, which are known to be a common structure element for a-C:HxDy and C60 systems. Higher energy states 8–13 eV are usually attributed to C2p s-states [2]. Photoluminescence experiments with tokamak flakes by using excitation of SR ‘‘white’’ X-ray beam (hoX5 keV) were performed at the XEOL station D’5.6 of the Siberia-2 SR source. Practically, no luminescence was observed in this case. However, an amorphous 2 mcm a-C:H film on a silicon substrate was excited by X-rays, resulting in luminescence at 450–650 nm with a maximum near 540 nm, which is different from the luminescence of real flakes in Fig. 1. We think this was effected due to X-ray excitation of a thick Si substrate (1 mm, with emission at 280–450 nm and a maximum at 340 nm), and the latter may serve as a source for a-C:H luminescence. On the contrary, X-ray excitation of deep carbon states C1s, C2s, are not effective for luminescence of tokamak flakes, where luminescence occurs only due to UV–VUV excitation, though the flake thickness is 10 times larger than that for a-C:H film. X-ray fluorescence and EXAFS investigations
manifested the presence of high Z absorbers Fe, Co, Ni, Cr, etc. as impurities [1], having a low p105 concentration, which cannot influence X-ray excitation. The EXAFS spectra of the Fe-K edge of flakes were obtained at the EXAFS Station of Siberian Synchrotron Radiation Center with the VEPP-3 SR source. The spectra were recorded under fluorescent mode, and were treated using standard procedures [6]. The radial distribution function (RDF) was calculated from the EXAFS spectra in k3w(k) as modulus of Fourier transform at the wave-number interval 3.5–10.2 A˚1. Curve-fitting procedure with EXCURV92 [7] code was employed to determine precisely the distances and coordination numbers. Debye–Waller factors are fixed (all values are equal to 0.005 A˚2). Curves of k3w(k) and RDF describing iron local arrangements are presented in Fig. 3. Curve-fitting procedure gives the following data: distance Fe–C ¼ 2.11 A˚, and corresponding coordination number is 6.2. Fe cations seemingly occupy octahedral positions with C surrounding. The mean Fe–C distance is typical for iron carbide, and there are no features of far Fe–Fe coordination spheres. Possibly, such Me–C clusters may lead to interconnection between the sp2 C–H clusters (luminescence centers), resulting in non-radiative recombination and quenching of luminescence induced by X-rays. Another possible explanation may be connected with decay of highly excited singlet states via triplet states, for example, like Sn–S1 and S1–T1 interconnection,
χ (k)* k3 (a.u.)
Fig. 2. Normalized luminescence excitation spectra for the tokamak films and fullerite C60 thin films at 300 K. The spectrum (dash-dot line) from Fig. 1 is shown for comparison.
227
0.00
_____ exper. _ __ theory
4.00 Distance ( Å)
8.00
Fig. 3. Results of curve-fitting procedure for EXAFS spectra of the Fe-K edge for the tokamak films.
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Fig. 4. UV reflection spectrum for the tokamak films annealed to 450 1C.
followed by non-radiative decay (scheme known for organic crystals). The UV reflection studies, shown in Fig. 4, were carried using Shimadzu UV–VIS spectrometer with an incident angle 51 for films annealed to 450 1C in a nitrogen atmosphere. The reflection manifested a small decrease from 200 nm (6.2 eV, reflectivity R ¼ 1:52%) to 400 nm (3.1 eV, R ¼ 1:25%) with a minimum near 300 nm, the spectrum being rather poorly structured. We think this picture is caused by a weak variation of the DOS in the range 3–6 eV for sp2 and mixed sp2+sp3 states of annealed films, i.e. defective states, possibly, having elements of a graphite-like structure (EgE0). The latter is confirmed by the film color transformation from reddish-gold (for non-baked films) to black (450 1C). Defect density for unpaired spin states for tokamak flakes, measured by an EPR spectrometer at RT [1], displayed a high spin density, 1019 cm3, which is typical for a-C:H films [8]. The g-values manifested a low level of spin space anisotropy with a low g-value, gE2.003. The defects with unpaired spins could be sp3 s-dangling bonds, sp2 isolated dangling bonds and p-states of sp2 clusters with an odd number of sites [2]. All these states are identified within the gap states and control the nonradiative recombination of electrons and holes, leading to quenching of luminescence at 450 1C.
The infrared spectra [1] displayed noticeable changes in the C–H, O–H sp2 and sp3 vibration modes upon annealing to 450 1C. However, the deuterium sp3 C–D stretch modes (2100– 2200 cm1) did not disappear after baking, but only slightly diminished in intensity due to a partial desorption of deuterium. However, the luminescence was almost quenched. Though the hydrogen isotope concentration for untreated films was high (D/C0.5, H/C0.3), this means that the observed luminescence is not connected directly with the C–D electronic states. We think the influence of deuterium may be of an indirect character. The observed [1] IR vibration modes of the sp3C–D2,3 and sp3C–H1,2,3 states refer to a dielectric matrix for the sp2C–H aromatic clusters, which may be responsible for luminescence in tokamak films. Since almost no deuterium was found in the sp2 aromatic modes, there is no deuterium in these aromatic clusters. We think that the destruction of the sp3 matrix at 450 1C, consisting of C–D and C–H states, together with formation of the sp2 graphitization-type layers from sp2C–H clusters, lead to formation of defect states enhancing a non-radiative recombination. As a result, the model for luminescence temperature quenching may be analogous, in general features, for a-C:H films and tokamak erosion films.
References [1] V.G. Stankevich, B.N. Kolbasov, N.Yu. Svechnikov, et al., Conference Proceedings Symposium I (Adv. Polymers), ICMAT-2003, Singapore, 2004, pp. I.8–13. [2] J. Robertson, Semicond. Sci. Technol. 18 (3) (2003) S12. [3] A. Foulani, J. Phys. D: Appl. Phys. 36 (2003) 394. [4] D. Curie, Luminescence of Crystals, Moscow, publ. Foreign literature, 1961. [5] C. Godet, M.N. Berberan-Santos, Diamond and Related Mater. 10 (2001) 168. [6] D.I. Kochubey, in: D.I. Kochubey (Ed.), EXAFS Spectroscopy of Catalysts, Nauka, Novosibirsk, 1992, pp. 5–99. [7] N. Binsted, J.V. Campbell, S.J. Gurman, P.C. Stephenson, EXCURV92 program, SERC Daresbury Laboratory, UK, 1991. [8] R.C. Barklie, M. Collins, S.R.P. Silva, Phys. Rev. B 61 (5) (2000) 3546.
Nuclear Instruments and Methods in Physics Research A 543 (2005) 225–228 www.elsevier.com/locate/nima
Spectroscopic investigations of smooth hydrocarbon deuterated erosion flakes deposited from tokamak T-10 deuterium plasma discharge N.Yu. Svechnikova, V.G. Stankevicha, A.M. Lebedeva,, K.A. Menshikova, B.N. Kolbasova, N.M. Kocherginskyb, D. Rajarathnamb, Yu. Kostetskib, S.N. Ivanovc, V.V. Kriventsovd a
Russian Research Center Kurchatov Institute, Moscow 123128, Russian Federation b Faculty of Engineering, National University of Singapore, Singapore c Physical Faculty, Moscow State University, Moscow, Russian Federation d Boreskov Institute of Catalysis, Novosibirsk 630090, Russian Federation Available online 5 March 2005
Abstract Investigations of smooth deuterated carbon erosion films co-deposited from deuterium plasma discharges inside the tokamak T-10 vacuum chamber were carried out using UV–VIS and X-ray photoluminescence, UV reflection, EXAFS, EPR, and temperature measurements. The influence of defective states on photoluminescence and its temperature quenching are discussed. r 2005 Elsevier B.V. All rights reserved. PACS: 78.55.m; 78.66.Tr; 73.61.Ph; 52.55.Pi Keywords: Luminescence; Reflection; a-C:H; EPR; EXAFS; Vibration modes
1. Introduction The operational safety of the International Thermonuclear Experimental Reactor (ITER) may be seriously affected by the erosion of Corresponding author. Tel.: +7 095 1969017;
fax: +7 095 1967538. E-mail address: [email protected] (A.M. Lebedev).
plasma-facing materials, resulting in the formation of smooth hydrogenated carbon films (‘‘flakes’’) codeposited from plasma discharges inside the vacuum chamber. Such films can accumulate large amounts of hydrogen isotopes H, D, T (radioactive), and require a difficult cleaning procedure of the walls, mechanical or thermal. Therefore, it is necessary to know the electronic structure of such new systems, which has not been studied earlier,
0168-9002/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2005.01.187
ARTICLE IN PRESS 226
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and it is also necessary to control the amounts of H-isotopes, since these strongly influence the electronic structure. The samples were smooth carbon erosion films with a high hydrogen isotope concentration (D/C0.5, H/C0.3), produced from D-plasma discharge of the tokamak T-10 operating in the RRC Kurchatov Institute [1]. The erosion films possess cracks and other defects causing their flaking and separation from the walls. The films are very brittle, concave shaped from the plasma side, with a 10 mm thickness and a 0.5 cm2 size. The analogous systems (but more simple) are known as amorphous a-C:H and a-C:D carbon films [2,3]. Their valence band structure is determined by a mixture of mainly sp3 (diamond-like) and sp2 (graphite-like) states, and this can be changed due to heating or defect formation. The sp2 clusters are known to form s and s extended states, and p-states localized inside a s–s gap, while sp2 clusters are imbedded in a dielectric sp3 matrix. For photon energies up to 6–8 eV, the absorption of light is described in terms of p–p transitions, and photoluminescence is attributed to electron–hole (e–h) recombination in the p-localized states of sp2 clusters. The defect states are identified within the band gap, and these control non-radiative recombination.
2. Experiments and discussion The photoluminescence spectra were taken at room temperature for the annealed samples at 200 and 450 1C, employing a PTI Instruments’ Quantamaster QM-5 Fluorescence system equipped with a pulsed xenon lamp source and a PMT detector. The normalized emission and luminescence excitation spectra are shown in Fig. 1 for 200 1C (as known for a-C:H films, annealing to T ¼ 1002200 1C may lead to some growth of luminescence intensity, due to H-saturation of carbon dangling bonds serving as non-radiative recombination centers [3]). The emission (under 372 nm excitation) is occupying the interval 390–600 nm (3.18–2.1 eV), and this has a certain structure with a maximum at 450 nm, and an FWHM ¼ 70 nm: Almost a mirror-like lumines-
Fig. 1. Normalized emission and luminescence excitation spectra of the tokamak film annealed to 200 1C.
cence excitation spectrum, taken under luminescence observation at 450 nm (2.76 eV), is occupying the interval 230–450 nm (5.4–2.8 eV) with a maximum near 370 nm (3.35 eV). These data indicate a gap value Eg3 eV. The Stokes shift is equal to 3.352.76 ¼ 0.59 eV. This rather weak overlapping of emission and excitation spectra, together with a noticeable Stokes shift ð0:59 eVbkT 0:025 eVÞ; point to a certain possibility for non-radiative recombination [4]. In principle, these spectra can be deconvoluted to 3–4 Gaussians. Similar spectra are typical of excitonic luminescence for a-C:H films [3]. A rather small bandwidth can be referred to a rather strong localization of photogenerated e–h pairs inside an sp2 cluster [5]. Photoluminescence was found to be almost quenched (to the background level) after baking to 450 1C in a nitrogen atmosphere, due to non-radiative energy dissipation caused, probably, by disordered sp2 aromatic network. In Fig. 2, the normalized luminescence excitation spectra of tokamak flakes and C60 thin films are shown. The measurements were performed at the Universal VUV spectrometer D’4.2 of the Siberia-1 SR source in the range of 3–10 eV at 300 K. Photoluminescence was registered with a FEU-100 PMT (maximum sensitivity near 420 nm). The excitation spectrum (dash-dot line) from Fig. 1, normalized to the first peak of the C60 curve is shown for comparison. This picture shows
ARTICLE IN PRESS N.Yu. Svechnikov et al. / Nuclear Instruments and Methods in Physics Research A 543 (2005) 225–228
___ __exper. _ _ _ theory
4.00 6.00 8.00 10.00 Wave number (Å-1)
Magnitude of FT (a.u.)
a definite similarity between excitation spectra of erosion films and those for C60. The tokamak peaks at 3.34, 5.47, 6.5 and 8.36 eV are close to the position of C60 peaks, and the latter refers to C2p p-states and to p þ s mixed states for C QC aromatic rings, which are known to be a common structure element for a-C:HxDy and C60 systems. Higher energy states 8–13 eV are usually attributed to C2p s-states [2]. Photoluminescence experiments with tokamak flakes by using excitation of SR ‘‘white’’ X-ray beam (hoX5 keV) were performed at the XEOL station D’5.6 of the Siberia-2 SR source. Practically, no luminescence was observed in this case. However, an amorphous 2 mcm a-C:H film on a silicon substrate was excited by X-rays, resulting in luminescence at 450–650 nm with a maximum near 540 nm, which is different from the luminescence of real flakes in Fig. 1. We think this was effected due to X-ray excitation of a thick Si substrate (1 mm, with emission at 280–450 nm and a maximum at 340 nm), and the latter may serve as a source for a-C:H luminescence. On the contrary, X-ray excitation of deep carbon states C1s, C2s, are not effective for luminescence of tokamak flakes, where luminescence occurs only due to UV–VUV excitation, though the flake thickness is 10 times larger than that for a-C:H film. X-ray fluorescence and EXAFS investigations
manifested the presence of high Z absorbers Fe, Co, Ni, Cr, etc. as impurities [1], having a low p105 concentration, which cannot influence X-ray excitation. The EXAFS spectra of the Fe-K edge of flakes were obtained at the EXAFS Station of Siberian Synchrotron Radiation Center with the VEPP-3 SR source. The spectra were recorded under fluorescent mode, and were treated using standard procedures [6]. The radial distribution function (RDF) was calculated from the EXAFS spectra in k3w(k) as modulus of Fourier transform at the wave-number interval 3.5–10.2 A˚1. Curve-fitting procedure with EXCURV92 [7] code was employed to determine precisely the distances and coordination numbers. Debye–Waller factors are fixed (all values are equal to 0.005 A˚2). Curves of k3w(k) and RDF describing iron local arrangements are presented in Fig. 3. Curve-fitting procedure gives the following data: distance Fe–C ¼ 2.11 A˚, and corresponding coordination number is 6.2. Fe cations seemingly occupy octahedral positions with C surrounding. The mean Fe–C distance is typical for iron carbide, and there are no features of far Fe–Fe coordination spheres. Possibly, such Me–C clusters may lead to interconnection between the sp2 C–H clusters (luminescence centers), resulting in non-radiative recombination and quenching of luminescence induced by X-rays. Another possible explanation may be connected with decay of highly excited singlet states via triplet states, for example, like Sn–S1 and S1–T1 interconnection,
χ (k)* k3 (a.u.)
Fig. 2. Normalized luminescence excitation spectra for the tokamak films and fullerite C60 thin films at 300 K. The spectrum (dash-dot line) from Fig. 1 is shown for comparison.
227
0.00
_____ exper. _ __ theory
4.00 Distance ( Å)
8.00
Fig. 3. Results of curve-fitting procedure for EXAFS spectra of the Fe-K edge for the tokamak films.
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Fig. 4. UV reflection spectrum for the tokamak films annealed to 450 1C.
followed by non-radiative decay (scheme known for organic crystals). The UV reflection studies, shown in Fig. 4, were carried using Shimadzu UV–VIS spectrometer with an incident angle 51 for films annealed to 450 1C in a nitrogen atmosphere. The reflection manifested a small decrease from 200 nm (6.2 eV, reflectivity R ¼ 1:52%) to 400 nm (3.1 eV, R ¼ 1:25%) with a minimum near 300 nm, the spectrum being rather poorly structured. We think this picture is caused by a weak variation of the DOS in the range 3–6 eV for sp2 and mixed sp2+sp3 states of annealed films, i.e. defective states, possibly, having elements of a graphite-like structure (EgE0). The latter is confirmed by the film color transformation from reddish-gold (for non-baked films) to black (450 1C). Defect density for unpaired spin states for tokamak flakes, measured by an EPR spectrometer at RT [1], displayed a high spin density, 1019 cm3, which is typical for a-C:H films [8]. The g-values manifested a low level of spin space anisotropy with a low g-value, gE2.003. The defects with unpaired spins could be sp3 s-dangling bonds, sp2 isolated dangling bonds and p-states of sp2 clusters with an odd number of sites [2]. All these states are identified within the gap states and control the nonradiative recombination of electrons and holes, leading to quenching of luminescence at 450 1C.
The infrared spectra [1] displayed noticeable changes in the C–H, O–H sp2 and sp3 vibration modes upon annealing to 450 1C. However, the deuterium sp3 C–D stretch modes (2100– 2200 cm1) did not disappear after baking, but only slightly diminished in intensity due to a partial desorption of deuterium. However, the luminescence was almost quenched. Though the hydrogen isotope concentration for untreated films was high (D/C0.5, H/C0.3), this means that the observed luminescence is not connected directly with the C–D electronic states. We think the influence of deuterium may be of an indirect character. The observed [1] IR vibration modes of the sp3C–D2,3 and sp3C–H1,2,3 states refer to a dielectric matrix for the sp2C–H aromatic clusters, which may be responsible for luminescence in tokamak films. Since almost no deuterium was found in the sp2 aromatic modes, there is no deuterium in these aromatic clusters. We think that the destruction of the sp3 matrix at 450 1C, consisting of C–D and C–H states, together with formation of the sp2 graphitization-type layers from sp2C–H clusters, lead to formation of defect states enhancing a non-radiative recombination. As a result, the model for luminescence temperature quenching may be analogous, in general features, for a-C:H films and tokamak erosion films.
References [1] V.G. Stankevich, B.N. Kolbasov, N.Yu. Svechnikov, et al., Conference Proceedings Symposium I (Adv. Polymers), ICMAT-2003, Singapore, 2004, pp. I.8–13. [2] J. Robertson, Semicond. Sci. Technol. 18 (3) (2003) S12. [3] A. Foulani, J. Phys. D: Appl. Phys. 36 (2003) 394. [4] D. Curie, Luminescence of Crystals, Moscow, publ. Foreign literature, 1961. [5] C. Godet, M.N. Berberan-Santos, Diamond and Related Mater. 10 (2001) 168. [6] D.I. Kochubey, in: D.I. Kochubey (Ed.), EXAFS Spectroscopy of Catalysts, Nauka, Novosibirsk, 1992, pp. 5–99. [7] N. Binsted, J.V. Campbell, S.J. Gurman, P.C. Stephenson, EXCURV92 program, SERC Daresbury Laboratory, UK, 1991. [8] R.C. Barklie, M. Collins, S.R.P. Silva, Phys. Rev. B 61 (5) (2000) 3546.