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Studies on modification of some first wall materials using 3–6.8 MeV He ions
Fusion Engineering and Design 49 – 50 (2000) 171 – 176 www.elsevier.com/locate/fusengdes
Studies on modification of some first wall materials using 3–6.8 MeV He ions B. Constantinescu a,*, C. Sarbu b b
a Institute for Atomic Physics, P.O. Box MG-6, Bucharest, Romania IFA-Institute for Physics and Technology of Materials, P.O. Box MG-7, Bucharest, Romania
Abstract Because very few results are reported in the MeV region, we have started a systematic investigation concerning the fluence and energy dependence of blistering induced in some useful materials for the first wall (stainless steels, Ni, Cu, Mo). They have been irradiated with 3.0, 4.7 and 6.8 MeV He ions. The irradiation effects have been investigated by means of a TEMSCAN-200-CX electron microscope and two metallographic microscopes. Irradiation phenomena as sponge- and wave-like structures, submicronic cracks, multilayer flaking, micro-conglomerates, secondary blisters, microcraters were observed. An interesting effect is the amorphous phase in the Ti-modified austenitic steel 12KH18N10T, phase formatted during irradiation with 6.8 MeV He+ ions up to a dose of crater occurrence (7×1018 ions per cm2), the temperature of specimens (100 mm thick) being maintained during irradiation in the range 30 – 60°C. The X-ray microanalysis shows the presence of the major alloy elements in the amorphous area, whereas in that embedding a microcrystallite it is to be noticed the Ni depletion and the presence of Si and Mo. A potential explanation of the energy dependence of average blisters diameter d and blister critical dose could be stressed-induced model, because, in our cases (medium energy He ions), d –t m, where t is the blister skin thickness. For our high energy data, an m=1.8 value is relatively convenient, except Mo, where m= 1.5 is more suitable. © 2000 Elsevier Science B.V. All rights reserved. Keywords: He ions; First wall; Electron microscope
1. Introduction Blistering has been the object of intense research in connection with the problem of developing a fusion reactor, since the first wall and the elements of the divertor will be subject to intense * Corresponding author. Tel.: +41-780-7040; fax: + 41423-1701/1650. E-mail address: [email protected] (B. Constantinescu).
bombardment of ions or fast charge-exchange neutrals of deuterium, tritium and also of helium, which is formed in the DT reaction [1]. A study of blistering is of major interest for both the materials science problems of fusion reactors and other applications in which materials are bombarded by ions of relatively insoluble gases. Up to now, the basic characteristics of blistering and exfoliation have been studied for bombardment by monoenergetic He ions, mainly below 1 MeV. Because very few results are reported for He ions in the
0920-3796/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 0 - 3 7 9 6 ( 0 0 ) 0 0 4 1 9 - 1
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
172
MeV region, we have started a systematic investigation [2] concerning the fluence and energy dependence of blistering induced in some potentially useful materials for the first wall, namely stainless steels, Ni, Cu, Mo. They have been irradiated with 3.0, 4.7 and 6.8 MeV a-particles accelerated in the subharmonic regime of the classical U-120 Cyclotron at the Institute of Atomic Physics [3]. These energy values are the most easily obtainable at our accelerator.
been 1.5–2.0× 1013 He per cm2·s for 3.0 MeV, 1.0–1.5×1013 He per cm2·s for 4.7 MeV, and for 6.8 MeV it has been only 0.3× 1013 He per cm2·s (that being a very unmanageable and unstable running regime of the Cyclotron). The angle of incidence beam — target has been 909 1° (perpendicular irradiation). The irradiation effects have been investigated by means of a TEMSCAN-200-CX electron microscope and two metallographic microscopes, an Orthoplan Pol Leitz and a PMG3-613V Olympus. The results are summarised in Table 1.
2. Experimental The irradiated samples have been foils of commercial materials having the following thickness, 100 mm for the Soviet 12KH18N10T (17 –19% Cr, 9–11% Ni, 2% Mn, 0.8% Ti) and the Japanese W-4541 (17– 19% Cr, 8.0 – 9.5% Ni, 0.6% Mn, 2% Ti) austenitic steels, 500 mm for the W-4016 (16.04% Cr, 0.13% Ni, 0.86% Mn) Romanian ferritic steel, 300 mm for the SS-304 (18 –20% Cr, 8–12% Ni, 2% Mn) Romanian austenitic steel and 100 mm for the pure metals Ni, Cu and Mo. During the irradiation-performed at the room temperature (30 – 50°C) — the beam intensity has
3. Results Two main phenomena have been observed as being dependent on the He irradiation fluence, blistering and flaking (craters formation). Blister appearance on the irradiated surface is almost instantaneous in the moment when the critical fluence (defined as a number of He atoms accumulated in the region where the a-particles are stopped — approximately at the end of their mean range) is reached.
Table 1 Samples, their irradiation conditions and summarised experimental results Material
Energy (MeV)
Fluence rate (×1013 He per cm2 s)
Critical fluence (×1018 He per cm2)
Average blister diameter (mm)
12KH18N10T
3.0 4.7 6.8 3.0 4.7 6.8 3.0 4.7 6.8 3.0 4.7 3.0 4.7 3.0 4.7 3.0 4.7
1.5 1.0 0.3 1.5 1.0 0.3 1.5 1.2 0.3 1.5 1.2 1.5 1.5 2.0 1.5 2.0 1.5
1.2 3.6 6.2 0.6 3.2 5.4 0.45 2.4 4.2 0.55 2.8 0.9 2.8 1.0 3.4 1.5 4.5
15. 500 1200a 140 500 1150a 120 450 1100a 130 450 140 480 140 500 500 1250a
W-4541
W-4016
SS-304 Ni Cu Mo
a
Single blister.
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
It was observed that isolated submicronic fissures along the boundaries of the grains belonging to the blister skin, and by increasing the irradiation fluence, the blisters opening and, finally, the occurrence of flaking. By increasing the fluence it is put into evidence the occurrence of larger (5– 20 mm in width) deep cracks having a length of hundreds of mm, then the blisters opening and, finally, the occurrence of flaking. Our experimental data are showing that the starting of the flaking phenomena occurs in the range of irradiation fluence from 1.5 ×1018 ions per cm2 (for W-4016) to 4.0× 1018 ions per cm2 (for Mo) in the case of 3.0 MeV incident ion energy, from 3.5×1018 ions per cm2 (for SS-304) to 8.0× 1018 ions per cm2 (for Mo) in the case of 4.7 MeV incident ion energy and finally, at about 6.0× 1018 ions per cm2 (for stainless steel) in the case of 6.8 MeV incident ion energy, see Table 1 and Fig. 1a–d. For investigating the inner side morphology aspects, the blisters have been mechanically opened by using a stainless steel pin. We have observed a lot of interesting aspects due to the irradiation, both on the bottom of the crater and on the inner side of its flaked skin, sponge- and wave-like structures; microcraters secondary small blisters; and multilayer flaking. Using TEM technique, microstructural changes as helium bubbles on matrix and grain boundaries, on loops and on TiC precipitates have been observed. A very interesting effect is an amorphous phase in the Ti-modified austenitic steel 12KH18N10T, phase formatted during irradiation with 6.8 MeV He+ ions up to a dose of crater occurrence (7× 1018 ions per cm2, beam density on target 0.3 – 0.8 mA), the temperature of specimens (100 mm thick) being maintained during irradiation in the 30 – 60°C range. The X-ray microanalysis shows the presence of the major alloy elements in the amorphous area, whereas in that embedding a microcrystallite it is to be noticed the Ni depletion and the presence of Si and Mo. To evaluate helium bubble, dislocation densities and mean bubble size, many photomicrographs are examined. Preliminary results in our cases show values of 5 × 1023 m − 3 and 2 ×10 − 15 m2 for bubble and dislocation densities, respectively,
173
and 45 9 10 and 90 9 30 nm for bubble diameter on matrix and grain boundaries, respectively.
4. Discussion A complete review on such phenomena, ‘Development of Surface Topography Due to Gas Ion Implantation’, is made by B.M.U. Scherzer [4]. Our cases belong to high fluence range of implantation (1021 –1024 ions per m2), where the amount of the gas trapped in the solid saturates, and, at the same time, the surface layer may be deformed into blisters and flakes due to internal gas pressure and lateral compressive stress. The appearance of blistering and flaking generally occurs at a well-defined critical fluence and is accompanied by the onset of reemission of the implanted gas. The origin and development of blisters and flakes were initially considered due to the action of high internal gas pressures in gas filled cavities alone. But the large swelling and the formation of lateral compressive stress accompanying gas ion implantation led some investigators to consider this stress well, presumably combined with the action of gas pressure in cavities, to explain the observed structures. Two stages of the process are considered, the formation of an interface of reduced strength between the surface layer and the bulk; the deformation of the surface layer. As initial stage models, we could mention critical swelling and interbubble fracture and loop punching models, developed by Evans [5], where the internal gas pressure is essential, but also the involvement of local stress depending on the range and damage distributions. As models of surface deformation, early models of blistering assume only forces due to the pressure of the included gas (spherical shell model, plastic deformation model). In Kaminsky and Das [6], because the existence of overpressurised gas bubbles and a suitable mechanism for bubble growth during the low temperature ion implantation are the essential ingredients for the validity of such a model, by taking into account the difference between the formation energy of helium interstitial and the
174
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
variation of the bubble free energy per every helium atom added, it is shown theoretically that such bubbles do indeed exist and, that their growth is driven by their bias for vacancies and by their anti-bias for interstitials.
Lateral compressive stress as an additional driving force of surface deformation has been introduced into blistering theory by Risch, Roth and Scherzer [7]. A variant is that of the integrated lateral stress — Guseva and Martynenko [8],
Fig. 1. Average blister diameter d (—) and critical fluence f (- - - - -) vs. blister skin thickness t; experimental data , ; t 3/2 (normalised to 3.0 MeV values) , "; t 2 (normalised to 3.0 MeV values) , +; (a) 12KH18N10T; (b) Ni; (c) Cu; (d) Mo ( and + values are practically identical).
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
175
Fig. 1. (Continued)
which suggests that the large lateral stresses troduced in the implanted layer lead to elastic instability and to the buckling of implanted surface layer from above
inan the the
weakened interface region. The model is based on the fact that, on the ground of the theory of plates, the displacement of a circular is given by:
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
176
W=
W0 (1−a)
(1)
where a = Sd 2/kN and W0 is the displacement of the plate center from the equilibrium position in the absence of an internal lateral stress (when S = 0), d is the plate diameter, N =Et 212(1 − n 2) is the stiffness of the plate, t is the thickness of the plate, E the Young’s modulus, n the Poisson’s ratio, and k is a coefficient depending on the boundary conditions (k=5.6 for an edge resting on a support or k = 19.6 for a pinned edge). The integrated stress is:
&
S = srr(x)dx
(2)
where srr(x) is the radial (lateral) stress at depth x. It can be seen from Eq. (1) that the plate becomes unstable even at a small value of W0, and that there is a transition to the plastic deformation when the denominator in Eq. (3) reaches the 0 value. It follows that at a constant value of S the blister diameter d is proportional to t 3/2, because: d=
n kN(t) S
1/2
(3)
Measurements by Das, Kaminsky and Fenske [9,10] for He in several models yielded for the relation d –t m values for m of 1.25 for Be, 0.85 for V, 1.15 for Ni and 1.22 for Nb at low energy, but 1.50 for high energy. In Fig. 1a – d, we represent our experimental values d for blisters diameter (see Table 1) versus the ‘deckeldicke’ (t $He ions range, for our highenergy values) for 12KH18N, Ni, Cu, Mo. We also present a dependence d – t 3/2 and a dependence d–t 2, both normalised to E = 3.0 MeV values (the dependence d – t is, evidently, too far from the experimental values). As is observed, for our highenergy data, m = 2 is a relatively convenient value, excepting Mo, where m =1.5 is more suitable.
To confirm the tendency of the m values to shift from 1 to 1.5 for low energy to 1.5–2 for high energy (see our data), we intend to enlarge the variety of samples (other metals and alloys resulting from various metallurgical preparation conditions) and of bombarding beams (other ions, with different energies).
References [1] R. Behrisch, M.U. Scherzer, He wall bombardment and wall erosion in fusion devices, Radiat. Eff. 78 (1983) 393 – 412. [2] B. Constantinescu, V. Florescu, C. Sarbu, Radiation damage and surface deformation effects on stainless steel produced by helium-ion bombardment, J. Nucl. Mater. 132 (1985) 105 – 109. [3] B. Constantinescu, S. Dima, E. Ivanov, D. Plostinaru, Elemental analysis using X and prompt g-rays induced by 4.7 MeV a-particles, Int. J. Radiat. Appl. Instrum. 37 (1) (1986) 53 – 60. [4] B.M.U. Scherzer, Sputtering by particle bombardment II, in: R. Behrish (Ed.), Topics in Applied Physics, vol. 52, Springer, Berlin, 1983, pp. 271 – 304. [5] H.M. Evans, Blister lid thickness measurements — a discussion in terms of the interbubble fracture model of blister formation, J. Nucl. Mater. 93/94 (1980) 745–752. [6] M. Kaminsky, S.K. Das, Surface damage of 316 stainless steel irradiated with 4He+ to high doses, J. Nucl. Mater. 76/77 (1978) 256 – 266. [7] M.R. Risch, J. Roth, B.M.U. Scherzer, Proceedings of the International Symposium on Plasma Wall Interaction Juelich, October 1976, Pergamon Press, London, 1977, pp. 391 – 423. [8] M.I. Guseva, Y.V. Martynenko, in: R.A. Johnson, A.N. Orlov (Eds.), Physics of Radiation Effects in Crystals, Elsevier, Amsterdam, 1986, pp. 621 – 648. [9] S.K. Das, M. Kaminsky, G. Fenske, The significance of a correlation of blister diameter with skin thickness for Ni and Be for blistering models, J. Nucl. Mater. 76/77 (1978) 215 – 224. [10] G. Fenske, S.K. Das, M. Kaminski, Depth distribution of bubbles in 4He+-ion irradiated nickel and the mechanism of blister formation, J. Nucl. Mater. 76/77 (1978) 247– 258.
Studies on modification of some first wall materials using 3–6.8 MeV He ions B. Constantinescu a,*, C. Sarbu b b
a Institute for Atomic Physics, P.O. Box MG-6, Bucharest, Romania IFA-Institute for Physics and Technology of Materials, P.O. Box MG-7, Bucharest, Romania
Abstract Because very few results are reported in the MeV region, we have started a systematic investigation concerning the fluence and energy dependence of blistering induced in some useful materials for the first wall (stainless steels, Ni, Cu, Mo). They have been irradiated with 3.0, 4.7 and 6.8 MeV He ions. The irradiation effects have been investigated by means of a TEMSCAN-200-CX electron microscope and two metallographic microscopes. Irradiation phenomena as sponge- and wave-like structures, submicronic cracks, multilayer flaking, micro-conglomerates, secondary blisters, microcraters were observed. An interesting effect is the amorphous phase in the Ti-modified austenitic steel 12KH18N10T, phase formatted during irradiation with 6.8 MeV He+ ions up to a dose of crater occurrence (7×1018 ions per cm2), the temperature of specimens (100 mm thick) being maintained during irradiation in the range 30 – 60°C. The X-ray microanalysis shows the presence of the major alloy elements in the amorphous area, whereas in that embedding a microcrystallite it is to be noticed the Ni depletion and the presence of Si and Mo. A potential explanation of the energy dependence of average blisters diameter d and blister critical dose could be stressed-induced model, because, in our cases (medium energy He ions), d –t m, where t is the blister skin thickness. For our high energy data, an m=1.8 value is relatively convenient, except Mo, where m= 1.5 is more suitable. © 2000 Elsevier Science B.V. All rights reserved. Keywords: He ions; First wall; Electron microscope
1. Introduction Blistering has been the object of intense research in connection with the problem of developing a fusion reactor, since the first wall and the elements of the divertor will be subject to intense * Corresponding author. Tel.: +41-780-7040; fax: + 41423-1701/1650. E-mail address: [email protected] (B. Constantinescu).
bombardment of ions or fast charge-exchange neutrals of deuterium, tritium and also of helium, which is formed in the DT reaction [1]. A study of blistering is of major interest for both the materials science problems of fusion reactors and other applications in which materials are bombarded by ions of relatively insoluble gases. Up to now, the basic characteristics of blistering and exfoliation have been studied for bombardment by monoenergetic He ions, mainly below 1 MeV. Because very few results are reported for He ions in the
0920-3796/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 0 - 3 7 9 6 ( 0 0 ) 0 0 4 1 9 - 1
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
172
MeV region, we have started a systematic investigation [2] concerning the fluence and energy dependence of blistering induced in some potentially useful materials for the first wall, namely stainless steels, Ni, Cu, Mo. They have been irradiated with 3.0, 4.7 and 6.8 MeV a-particles accelerated in the subharmonic regime of the classical U-120 Cyclotron at the Institute of Atomic Physics [3]. These energy values are the most easily obtainable at our accelerator.
been 1.5–2.0× 1013 He per cm2·s for 3.0 MeV, 1.0–1.5×1013 He per cm2·s for 4.7 MeV, and for 6.8 MeV it has been only 0.3× 1013 He per cm2·s (that being a very unmanageable and unstable running regime of the Cyclotron). The angle of incidence beam — target has been 909 1° (perpendicular irradiation). The irradiation effects have been investigated by means of a TEMSCAN-200-CX electron microscope and two metallographic microscopes, an Orthoplan Pol Leitz and a PMG3-613V Olympus. The results are summarised in Table 1.
2. Experimental The irradiated samples have been foils of commercial materials having the following thickness, 100 mm for the Soviet 12KH18N10T (17 –19% Cr, 9–11% Ni, 2% Mn, 0.8% Ti) and the Japanese W-4541 (17– 19% Cr, 8.0 – 9.5% Ni, 0.6% Mn, 2% Ti) austenitic steels, 500 mm for the W-4016 (16.04% Cr, 0.13% Ni, 0.86% Mn) Romanian ferritic steel, 300 mm for the SS-304 (18 –20% Cr, 8–12% Ni, 2% Mn) Romanian austenitic steel and 100 mm for the pure metals Ni, Cu and Mo. During the irradiation-performed at the room temperature (30 – 50°C) — the beam intensity has
3. Results Two main phenomena have been observed as being dependent on the He irradiation fluence, blistering and flaking (craters formation). Blister appearance on the irradiated surface is almost instantaneous in the moment when the critical fluence (defined as a number of He atoms accumulated in the region where the a-particles are stopped — approximately at the end of their mean range) is reached.
Table 1 Samples, their irradiation conditions and summarised experimental results Material
Energy (MeV)
Fluence rate (×1013 He per cm2 s)
Critical fluence (×1018 He per cm2)
Average blister diameter (mm)
12KH18N10T
3.0 4.7 6.8 3.0 4.7 6.8 3.0 4.7 6.8 3.0 4.7 3.0 4.7 3.0 4.7 3.0 4.7
1.5 1.0 0.3 1.5 1.0 0.3 1.5 1.2 0.3 1.5 1.2 1.5 1.5 2.0 1.5 2.0 1.5
1.2 3.6 6.2 0.6 3.2 5.4 0.45 2.4 4.2 0.55 2.8 0.9 2.8 1.0 3.4 1.5 4.5
15. 500 1200a 140 500 1150a 120 450 1100a 130 450 140 480 140 500 500 1250a
W-4541
W-4016
SS-304 Ni Cu Mo
a
Single blister.
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
It was observed that isolated submicronic fissures along the boundaries of the grains belonging to the blister skin, and by increasing the irradiation fluence, the blisters opening and, finally, the occurrence of flaking. By increasing the fluence it is put into evidence the occurrence of larger (5– 20 mm in width) deep cracks having a length of hundreds of mm, then the blisters opening and, finally, the occurrence of flaking. Our experimental data are showing that the starting of the flaking phenomena occurs in the range of irradiation fluence from 1.5 ×1018 ions per cm2 (for W-4016) to 4.0× 1018 ions per cm2 (for Mo) in the case of 3.0 MeV incident ion energy, from 3.5×1018 ions per cm2 (for SS-304) to 8.0× 1018 ions per cm2 (for Mo) in the case of 4.7 MeV incident ion energy and finally, at about 6.0× 1018 ions per cm2 (for stainless steel) in the case of 6.8 MeV incident ion energy, see Table 1 and Fig. 1a–d. For investigating the inner side morphology aspects, the blisters have been mechanically opened by using a stainless steel pin. We have observed a lot of interesting aspects due to the irradiation, both on the bottom of the crater and on the inner side of its flaked skin, sponge- and wave-like structures; microcraters secondary small blisters; and multilayer flaking. Using TEM technique, microstructural changes as helium bubbles on matrix and grain boundaries, on loops and on TiC precipitates have been observed. A very interesting effect is an amorphous phase in the Ti-modified austenitic steel 12KH18N10T, phase formatted during irradiation with 6.8 MeV He+ ions up to a dose of crater occurrence (7× 1018 ions per cm2, beam density on target 0.3 – 0.8 mA), the temperature of specimens (100 mm thick) being maintained during irradiation in the 30 – 60°C range. The X-ray microanalysis shows the presence of the major alloy elements in the amorphous area, whereas in that embedding a microcrystallite it is to be noticed the Ni depletion and the presence of Si and Mo. To evaluate helium bubble, dislocation densities and mean bubble size, many photomicrographs are examined. Preliminary results in our cases show values of 5 × 1023 m − 3 and 2 ×10 − 15 m2 for bubble and dislocation densities, respectively,
173
and 45 9 10 and 90 9 30 nm for bubble diameter on matrix and grain boundaries, respectively.
4. Discussion A complete review on such phenomena, ‘Development of Surface Topography Due to Gas Ion Implantation’, is made by B.M.U. Scherzer [4]. Our cases belong to high fluence range of implantation (1021 –1024 ions per m2), where the amount of the gas trapped in the solid saturates, and, at the same time, the surface layer may be deformed into blisters and flakes due to internal gas pressure and lateral compressive stress. The appearance of blistering and flaking generally occurs at a well-defined critical fluence and is accompanied by the onset of reemission of the implanted gas. The origin and development of blisters and flakes were initially considered due to the action of high internal gas pressures in gas filled cavities alone. But the large swelling and the formation of lateral compressive stress accompanying gas ion implantation led some investigators to consider this stress well, presumably combined with the action of gas pressure in cavities, to explain the observed structures. Two stages of the process are considered, the formation of an interface of reduced strength between the surface layer and the bulk; the deformation of the surface layer. As initial stage models, we could mention critical swelling and interbubble fracture and loop punching models, developed by Evans [5], where the internal gas pressure is essential, but also the involvement of local stress depending on the range and damage distributions. As models of surface deformation, early models of blistering assume only forces due to the pressure of the included gas (spherical shell model, plastic deformation model). In Kaminsky and Das [6], because the existence of overpressurised gas bubbles and a suitable mechanism for bubble growth during the low temperature ion implantation are the essential ingredients for the validity of such a model, by taking into account the difference between the formation energy of helium interstitial and the
174
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
variation of the bubble free energy per every helium atom added, it is shown theoretically that such bubbles do indeed exist and, that their growth is driven by their bias for vacancies and by their anti-bias for interstitials.
Lateral compressive stress as an additional driving force of surface deformation has been introduced into blistering theory by Risch, Roth and Scherzer [7]. A variant is that of the integrated lateral stress — Guseva and Martynenko [8],
Fig. 1. Average blister diameter d (—) and critical fluence f (- - - - -) vs. blister skin thickness t; experimental data , ; t 3/2 (normalised to 3.0 MeV values) , "; t 2 (normalised to 3.0 MeV values) , +; (a) 12KH18N10T; (b) Ni; (c) Cu; (d) Mo ( and + values are practically identical).
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
175
Fig. 1. (Continued)
which suggests that the large lateral stresses troduced in the implanted layer lead to elastic instability and to the buckling of implanted surface layer from above
inan the the
weakened interface region. The model is based on the fact that, on the ground of the theory of plates, the displacement of a circular is given by:
B. Constantinescu, C. Sarbu / Fusion Engineering and Design 49–50 (2000) 171–176
176
W=
W0 (1−a)
(1)
where a = Sd 2/kN and W0 is the displacement of the plate center from the equilibrium position in the absence of an internal lateral stress (when S = 0), d is the plate diameter, N =Et 212(1 − n 2) is the stiffness of the plate, t is the thickness of the plate, E the Young’s modulus, n the Poisson’s ratio, and k is a coefficient depending on the boundary conditions (k=5.6 for an edge resting on a support or k = 19.6 for a pinned edge). The integrated stress is:
&
S = srr(x)dx
(2)
where srr(x) is the radial (lateral) stress at depth x. It can be seen from Eq. (1) that the plate becomes unstable even at a small value of W0, and that there is a transition to the plastic deformation when the denominator in Eq. (3) reaches the 0 value. It follows that at a constant value of S the blister diameter d is proportional to t 3/2, because: d=
n kN(t) S
1/2
(3)
Measurements by Das, Kaminsky and Fenske [9,10] for He in several models yielded for the relation d –t m values for m of 1.25 for Be, 0.85 for V, 1.15 for Ni and 1.22 for Nb at low energy, but 1.50 for high energy. In Fig. 1a – d, we represent our experimental values d for blisters diameter (see Table 1) versus the ‘deckeldicke’ (t $He ions range, for our highenergy values) for 12KH18N, Ni, Cu, Mo. We also present a dependence d – t 3/2 and a dependence d–t 2, both normalised to E = 3.0 MeV values (the dependence d – t is, evidently, too far from the experimental values). As is observed, for our highenergy data, m = 2 is a relatively convenient value, excepting Mo, where m =1.5 is more suitable.
To confirm the tendency of the m values to shift from 1 to 1.5 for low energy to 1.5–2 for high energy (see our data), we intend to enlarge the variety of samples (other metals and alloys resulting from various metallurgical preparation conditions) and of bombarding beams (other ions, with different energies).
References [1] R. Behrisch, M.U. Scherzer, He wall bombardment and wall erosion in fusion devices, Radiat. Eff. 78 (1983) 393 – 412. [2] B. Constantinescu, V. Florescu, C. Sarbu, Radiation damage and surface deformation effects on stainless steel produced by helium-ion bombardment, J. Nucl. Mater. 132 (1985) 105 – 109. [3] B. Constantinescu, S. Dima, E. Ivanov, D. Plostinaru, Elemental analysis using X and prompt g-rays induced by 4.7 MeV a-particles, Int. J. Radiat. Appl. Instrum. 37 (1) (1986) 53 – 60. [4] B.M.U. Scherzer, Sputtering by particle bombardment II, in: R. Behrish (Ed.), Topics in Applied Physics, vol. 52, Springer, Berlin, 1983, pp. 271 – 304. [5] H.M. Evans, Blister lid thickness measurements — a discussion in terms of the interbubble fracture model of blister formation, J. Nucl. Mater. 93/94 (1980) 745–752. [6] M. Kaminsky, S.K. Das, Surface damage of 316 stainless steel irradiated with 4He+ to high doses, J. Nucl. Mater. 76/77 (1978) 256 – 266. [7] M.R. Risch, J. Roth, B.M.U. Scherzer, Proceedings of the International Symposium on Plasma Wall Interaction Juelich, October 1976, Pergamon Press, London, 1977, pp. 391 – 423. [8] M.I. Guseva, Y.V. Martynenko, in: R.A. Johnson, A.N. Orlov (Eds.), Physics of Radiation Effects in Crystals, Elsevier, Amsterdam, 1986, pp. 621 – 648. [9] S.K. Das, M. Kaminsky, G. Fenske, The significance of a correlation of blister diameter with skin thickness for Ni and Be for blistering models, J. Nucl. Mater. 76/77 (1978) 215 – 224. [10] G. Fenske, S.K. Das, M. Kaminski, Depth distribution of bubbles in 4He+-ion irradiated nickel and the mechanism of blister formation, J. Nucl. Mater. 76/77 (1978) 247– 258.