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Recrystallization of Kr in Kr-implanted and annealed aluminum
Journal of Nuclear Materials 203 (1993) 269-274 North-Holland
Recrystallization
of Kr in Kr-implanted
and annealed aluminum
I. Hashimoto ‘, J. Mitani a, Y. Miyazaki ‘, H. Yamaguchi ‘, E. Yagi b and M. Iwaki b a Department of Physics, Faculty of Science, Science Universiry of Tokyo, Shinjuku-ku, Tokyo 162, Japan ’ The Institute of Physical and Chemical Research, Wako-shi, Saitama 351-01, Japan
Received 4 December 1992; accepted 30 April 1993
Thin Al foils are implanted with 50 keV Kr ions at room temperature to a dose of 1 X 10’” Kr+ ions/cm’. Kr bubbles in an as-implanted specimen and also in an annealed specimen at 673 K have been examined for 10 mitt by transmission electron microscopy at temperatures between 140 and 300 K. A b&modal size distribution is observed in the annealed specimen, while a single-size distribution is observed in the as-implanted specimen. The lattice parameter of solid fee Kr in the as-implanted specimen is almost constant during cooling, whereas in the annealed one it increases gradually during cooling down to about 190 K and then becomes nearly constant. These parameters are briefly discussed from the view point of the phase transition of highly pressurized Kr.
1. Introduction Rare gas atoms implanted in metals have a low solubility [ll and precipitate into microclusters 12-41. The precipitates are often referred to as bubbles. From the analysis of Ronchi [S], the pressure in the bubbles has been estimated to be of the order of several GPa. Therefore, the bubbles formed by relatively heavy rare gases such as Ar, Kr and Xe are believed to precipitate as a crystalline solid and are aligned epitaxially with fee in an fee host metal at room temperature [6-S]. By in-situ heating experiments in an electron microscope, the melting of the bubbles during heating and the solidification in epitaxial regrowth during cooling have been observed [4,9-l 11. In the specimen ion-implanted at temperatures of 673 K or higher, the precipitation of Kr atoms injected in Ni evolves into a bi-modal size distribution containing small solid precipitates and an additional population of larger, faceted bubbles [12,13]. It is suggested that the swelling in these high gas production rate experiments is primarily controlled by a gas-driven mechanism and that the solid precipitates are immobile, while the larger bubbles move by surface diffusion during the implantation. In contrast with the above mentioned higher temperature injection experiment, Andersen et al. 1141 have carried out an X-ray diffraction experiment on 0022-3115/93/$06.00
cooling of Al single crystals implanted with Kr ions at room temperature. They have suggested to be a bimodal size distribution of bubbles in an annealed specimen up to 620 K and subsequently cooled to 12 K. They have also shown that the larger bubbles estimated to be 9 nm in average size melt at temperatures from 114 to 118 K, whereas smaller bubbles of 3.5 nm remain solids up to 600 K. However, up to the present, the detailed examination by TEM on the size distribution of Kr bubbles in Al has not been carried out yet. In this paper, we will check the state and the size distribution of Kr bubbles both in as-implanted and annealed specimens by means of TEM, and the growth of bubbles during annealing will be discussed. Furthermore, the recrystallization of Kr atoms during cooling will be discussed in terms of the electron diffraction.
2. Experimental procedure Thin Al single crystals were prepared by the strain annealing method from 5-N Al ingots. They were polished by the usual chemical and electrolytical thinning methods [81. The thin foils were implanted with 50 keV at room temperature in vacuum less than 1 x 10e6 Torr to a fluence of 1 x lOi Kr+ ions/cm2. The implantation of Kr ions was carried out by using a Riken low-current implanter with a flux of 1.7 x 10”
0 1993 - Elsevier Science Publishers B.V. All rights reserved
270
I. H~shi~o~o et al. / Rec~sialliza~ion of Kr in Al
Kr+ ions/cm2 s focusing on the target area of 3.3 X 3.3 cm*. This is sufficient to make a dense distribution of solid Kr bubbles. In general, the bright field images of the electron microscopy are used to the direct observation of lattice defects in crystals, while the dark field ones, if the extra electron diffraction reflections from the precipitate in crystals are obtained, have been used to know the distributions of the crystalline precipitates [9]. In our case, if larger bubbles are melting and smaller ones keep solid at room temperature, the size distribution of liquid and solid bubbles both in as-implanted and annealed specimens can be examined directly in comparison with the bright and dark field images taken by the reflection from the solid precipitates. So, at first, we took the bright and dark field images of Kr bubbles in both as-implanted foils and those after annealing at 673 K for 10 mm outside the electron microscope. The latter image was taken by using
the Kr (002) diffracted beams from Kr atoms. The diameter and the density of Kr bubbles were estimated from those images. The cooling experiment for two kinds of specimens was carried out. One was as-implanted and the other was annealed at 673 K for 10 min in vacuum after implantation. Those specimens were observed with a Hitachi H-800 transmission electron microscope attached with a cooling stage of liquid nitrogen operating at 100 kV. The specimens were set to the (100) directions by controlling its orientation and the diffraction reflections observed continuously throughout the cooling experiment. The temperature range was 140-300 K and the intensities of reflections were measured by a microdensitometer. The lattice parameter of Kr was measured from electron diffraction patterns by the simple ratio method [4] between (002) reflections and/or its systematic reflections from Al and Kr atoms. Here the lattice parameter of Al was nearly constant
Fig. 1. Typical electron micrographs of Kr bubbles. Here, (a) and (b) respectively show the bright field image and dark field one taken by the (002) reflection from Kr atoms in an as-implanted specimen. Cc) and Cd) are similar ones using the specimen after annealing at 673 K for 10 min, respectively.
271
I. Hashimotoet al. / Recrystallization of Kr in Al
2
4
6 RO Bubble D ismster
2
4
6
8
[Iml
Fig. 2. Size distributions of Kr bubbles. Here, the opened and the oblique-lined areas represent the relations between the number of bubbles estimated from the bright or the dark field images and their diameter, respectively, and the cross-hatched area is the overlapping part in both images. (a) In the as-implanted state, (b) after annealing at 673 K for 10 min.
during cooling and then the lattice parameter of Kr was determined in comparison with the lattice parameter of Al, a, = 0.4049 nm.
3. Experimental results
as in liquid or gas bubbles during their formation process. On the other hand, the size distributions in the bright and the dark field images of the specimen after annealing at 673 K for 10 min are shown in fig. 2b. Each of the distribution is separated. The mean diameter of smaller bubbles is 2.5 nm, which is the same value as that of the as-implanted one. Combining the bright field image with the dark field one, a b&modal size distribution is obtained where the bubbles larger than 4 nm in diameter are not observed in the dark field images. This shows that the critical size of liquid-solid phase transition of Kr bubbles is around 4 nm in diameter. The total density of Kr bubbles in the bright field image is 1.81 X 10’2/cm2 and the dark field one is 2.05 X 1012/cm2. The overlapped number of Kr bubbles shown by the cross-hatched area in fig. 2b is 2.07 x lO”/cm’. The density of Kr bubbles observed in the as-implanted specimen is 3.14 x 10*2/cm2 as mentioned before and that in the annealed one is 3.65 X 10r2/cmZ and then the density of bubbles increases during annealing. It is noted that a bi-modal size distribution with two maxima at 2.4 and 4.4 nm in diameter is observed in the annealed specimen, whereas there is a single size distribution in the as-implanted specimen. 3.2. Electron di~ruc~i~~
Fig. 1 shows the typical electron micrographs of Kr bubbles. Here, (a)-(d) are the same area, (a) and (b) show the bright field image and the dark field one taken by the (002) reflection from Kr atoms in an as-implanted specimen and (cl and (d) in the specimen after the annealing, respectively. The size distribution of solid Kr bubbles in the specimen from the dark field images taken by the (002) reflection of Kr atoms are shown in fig. 2. Here, opened and oblique-lined areas in the bar graphs show the number of bubbles and their diameter estimated from the bright or the dark field images, respectively, and the cross-hatched area is overlapped ones. The fairly sharp continuous size distribution around the mean diameter of Kr bubbles observed in the bright field image in an as-implanted specimen is nearly the same as that in the dark field image as shown in fig. 2a. The projected densities and the mean diameters are 3.14 X lO’*/cm*, 2.6 nm and 2.26 x 10’z/cm2, 2.5 nm, respectively. We note here that the number of Kr bubbles less than 2.6 nm in diameter is almost the same as in bright and dark field images, while the number of larger one decreases more than 45%. The fact shows that at least a part of these Iarger bubbles more than 2.6 nm in diameter is existing
The cooling experiment of Kr bubbles is carried out in the transmission electron microscope attached with a cooling stage of liquid nitrogen at the temperature ranging from 140 to 300 IL Fig. 3 shows the microdensitometric intensity around (002) diffraction spots of Al for the specimen after annealing at 673 K for 10 min. Here, the curves 1, 2 and 3 show the intensities at
-.270 _______ 197 K I( 139 K
I
Kr
Fig. 3. The microdensitometric intensity distribution around the (002) diffraction spot of Al.
212
I. Hashimotoet al. / Recrystallization of Kr in Al
l
as-implanted
The lattice parameter in an as-implanted specimen is almost constant during cooling down to 140 K as shown in fig. 4. The fact shows that the recrystallization of bubbles in the liquid or gas state in an as-implanted specimen is unexpected to occur during cooling. 4.2. Annealed specimen
Temperature
[Kl
Fig. 4. A change in lattice parameter of Kr during cooling. The lines are drawn only as a guide to the eyes.
278, 197 and 139 K, respectively. The small peak from
Kr atoms is observed apart from the Al (002) spot in the figure. This shows that the Kr atoms precipitate to have an fee lattice epitaxially aligned with the host Al matrix. It is noted here that the intensity of the (002) Kr diffraction reflection increases drastically by cooling the specimen and the integrated intensity ratio is estimated to be 1139/1278= 2.9. This shows that the number of solid Kr bubbles increases during cooling. In this case, the peak position moves towards the center of diffraction reflections (the left hand side), reflecting an increase in the lattice parameter. This is consistent with the result described below. The lattice parameter change during the cooling experiment is shown in fig. 4. Here, solid and open circles show the lattice parameters in an as-implanted specimen and in the annealed one, respectively. The lattice parameter of 0.551 nm is constant in an as-implanted specimen, while in the annealed one, it changes from 0.560 to 0.571 nm during the cooling from 300 to 190 K and becomes almost constant less than 190 K. This shows that the Kr bubbles in a solid phase are constant in an as-implanted specimen, whereas in an annealed one, some of the bubbles would be recrystallized into a solid phase with lowering the temperature depending on the bubble size. The results will be discussed in the next section.
4. Discussions 4.1. As-implanted specimen
As already shown in fig. 2a, almost all bubbles less than 2.6 nm in diameter are in solid, while larger bubbles are in solid by about 55% and then the remaining part is existing as in the liquid or gas state.
Fig. 5 shows the phase diagram of Kr calculated by the empirical Simon’s equation modified by Hardy et al. [15-171. The equation is P=A(T-
7’,,)C-B,
(1)
where P is the melting pressure at the absolute temperature T. A, B, C and T,, are constants and T, = 38.096 (K), A = 3.36253 X low4 (GPa), B = 0.177871 (GPa) and C = 1.44084 for Kr, respectively. The solid line shows the melting curve and the upper part of the line is a solid phase and the lower one is a liquid phase. The dotted lines are the isochore lines and show the relation between pressure and temperature estimated by the analysis of Ronchi [5] as a parameter of the molar volume (cm3/mol in unit) which is shown in the figure. Now, let us consider the relation between diameter and phase transition of Kr bubbles. According to the experimental results as shown in figs. 2a and 4, we assume here that the lattice parameter of Kr is initially equal to 0.551 nm (the molar volume I/ = 25.2 cm3/mol) and that the diameters of bubbles are 2.6 nm. If the molar volume of Kr changes only by the absorption of
100
200 Temperature
300
4 0 Kl
Fig. 5. The phase diagram of Kr atoms calculated by the empirical Simon’s equation modified by Hardy et al. [16]. The solid line shows the melting curve and the upper part of the line is the solid phase and the lower one is the liquid phase. The dotted lines are the isochore lines and are explained in the text. The numbers in the figure indicate the molar volume of Kr atoms and have cm3/mol in unit.
I. Hashimoto et al. / Recrystallization of Kr in Al
vacancies during annealing to the values as shown in fig. 5, the diameters of bubbles will change to 2.7, 2.8 and 2.9 nm in diameter, respectively. Here, the volume change on melting [15] is ignored. The diagram can give us the following conclusions. (A) Seeing a calculated line of 25.2 cm3/mol (2.6 nm in diameter), it is found that Kr bubbles are to be a solid phase at temperatures between 140-300 K. This is confirmed by the observation of as-implanted specimens. That is: (i) Almost all Kr bubbles around 2.6 nm in diameter can be observed on both bright and dark field images (fig. 2a). (ii) The lattice parameter is nearly constant independent of the cooling temperature (fig. 4). (B) If the number of Kr atoms in the bubble keeps constant, the solid Kr bubbles will easily be melting by the growth of only 0.2 nm or so in diameter by absorbing excess vacancies during annealing. For example, when the solid bubbles having 2.6 nm in diameter grow up to 2.8 nm, the molar volume changes to 31.4 cm3/mol and those grown-up bubbles are in liquid at room temperature. Non-conservation of the density of bubbles between as-implanted and annealed specimens as mentioned in section 3.1. is considered as follows. In our early experiment [18], we have observed electron diffraction patterns and electron micrographs obtained at room temperature on the 1 X 1015 Kr+ ions/cm* implanted specimen after annealing at 683 K for 30 min. It was shown that small bubbles were grown during annealing and a bi-modal size distribution appeared. If non-observable small bubbles in an as-implanted specimen are grown by absorbing vacancies during annealing, they become observable so as to increase bubble density. The integrated intensity of diffraction reflections from the Kr+ atoms as shown in fig. 3 increases during cooling. The value at 139 K is stronger by about 3 times than that of the room temperature. Since the integrated intensity of diffraction reflections is proportional to the cube of the number of Kr atoms [19], if the bubbles have the same molar volume and if all the bubbles up to around 4.0 nm in diameter observed in the bright field image shown in fig. 2b are recrystallized during cooling, the increment of the above diffraction reflections can be explained. In this case, the effect of the Debye-Wailer factor is ignored, because of a small value less than 1% [20]. The lattice parameter of the annealed specimen is increased about 0.01 nm during cooling from 300 to 190 K as shown in fig. 4. This is responsible for the recrystallization of bubbles up to around 4 nm in diameter in fig. 2b.
273
Rest and Birtcher [13] have carried out a rate theory approach to interpret observations on the precipitation of Kr, Xe and Ar injected into Ni at temperatures between 398 and 833 K. At temperatures of 673 K or higher, the implanted Kr bubbles evolve into a bi-modal size distribution containing small solid bubbles and an additional population of larger, faceted bubbles. The calculation explores the dependence of the Kr bi-modal size distribution on the maximum size of the solid Kr bubbles and on the bubble mobility. They have suggested that the solid Kr bubbles less than 4 nm in diameter are immobile during high temperature implantation at 773 K in Ni. From our experimental results shown in figs. 2a and 2b, the diameter of moving bubble can be considered to be 3-4 nm, because the density of bubbles larger than these sizes in the bright field images increases after annealing. A part of bubbles larger than 4 nm in diameter is made by the coalescence of 3-4 nm bubbles. When the coalesced bubbles are in solid during cooling, the lattice parameters of Kr are increased with their diameters, because of the difference in the equilibrium pressure before and after the coalescence. Since the solid bubbles of various sizes are distributed in the specimen, the lattice parameter may continuously increase during cooling and the intensity of diffraction spot contrasts is also increased during cooling. In the annealed specimen as shown in fig. 2b, the dark field images do not show the solid bubbles larger than 4 nm. On the other hand, the larger bubbles obtained by Andersen et al. [14] (their estimation is 9 nm in size) melt at temperatures from 114 to 118 K. This is near by the triple point temperature for Kr, 115.763 K. Similar calculations as shown in fig. 5 show again that the melting temperature of bubbles larger than 4 nm in diameter does not depend strongly on their sizes and almost all bubbles of any sizes larger than 4 nm in diameter observed in fig. 2b could be considered to melt at around 115 K. These facts suggest that the heterogeneous growth may occur during annealing by reflecting the heterogeneous density distributions in the specimen and the fairly wide range size distributions may be formed by the annealing.
5. Conclusions (1) From the results obtained by TEM observation of as-implanted foils at room temperature, it follows that almost all bubbles less than 2.6 nm in diameter are solid, while those of larger ones are coexisting in the liquid and the solid phase.
I. Hashimoto et al. / Recrystallization of Kr in AI
214
(2) In the foils annealed at 673 K for 10 min, from the changes of Kr lattice parameter and the integrated intensity of diffraction reflections with cooling temperature, the recrystallization occurs from an early stage of the cooling. (3) The bi-modal size distribution of Kr bubbles constructed with the solid and liquid or gas phases could be clearly observed by TEM.
References
Rimmer and A.H. Cottrell, Philos. Mag. 2 (1957) 1345. [2] A. vom Felde, J. Fink, Th. Miiller-Heinzerling, J. Pfliiger,
[l] D.E.
[3] [4] [S] [6] [7] [S]
B. Scheerer, G. Linker and D. Kaletta, Phys. Rev. Lett. 53 (1984) 922. C. Templier, C. Jaouen, J.P. Rivikre, J. Delafond and J. GrilhC, C.R. Acad. Sci. Paris 299 (1984) 613. J.H. Evans and D.J. Mazey, J. Phys. F15 (1985) Ll; Scripta Metall. 19 (1985) 621. C. Ronchi, J. Nucl. Mater. 96 (1981) 314. R.C. Birtcher and W. Jiger, J. Nucl. Mater. 135 (1985) 214. C.J. Rossouw and SE. Donnelly, Phys. Rev. Lett. 55 (1985) 2960. K. Takaishi, T. Kikuchi, K. Furuya, I. Hashimoto, H.
[9] [lo] [ll] [12] [13] [14]
[15]
[16] [17] [18] [19]
[20]
Yamaguchi, E. Yagi and M. Iwaki, Phys. Status Solidi 95 (1986) 135. R.C. Birtcher and W. Jgger, Ultramicroscopy 22 (1987) 261. J.H. Evans and D.J. Mazey, J. Nucl. Mater. 138 (1986) 16. G.L. Zhang and L. Niesen, J. Phys. Condens. Mater. 1 (1989) 1145. R.C. Birtcher and A.S. Liu, J. Nucl. Mater. 165 (1989) 101. J. Rest and R.C. Birtcher, J. Nucl. Mater. 168 (1989) 312. H.H. Andersen, J. Bohr, A. Johansen, E. Johnson, L. Sarholt-Kristensen and V. Surganov, Phys. Rev. Lett. 59 (1987) 1589. Rare Gas Solids, eds. M.L. Klein and J.A. Venables, (Academic Press, London, New York, San Francisco, 1976) pp. 63-728. W.H. Hardy II, R.K. Crawford and W.B. Daniels, J. Chem. Phys. 54 (1971) 1005. J.C. Desoyer, C. Templier, J. Delafond and H. Garem, Nucl. Inst. Meth. Phys. Res. B19/20 (1987) 450. E. Yagi, I. Hashimoto and H. Yamaguchi, J. Nucl. Mater. 169 (1989) 158. Electron Microscopy of Thin Crystals, P.B. Hirsch, eds. A. Howie, R.B. Nicholson, D.W. Pashley and M.J. Whelan (Butterworths, London, 1965). International Tables for X-Ray Crystallography, eds. N.F. M. Henry and K. Lonsdale (Kynoch Press, Birmingham, England, 1969).
Recrystallization
of Kr in Kr-implanted
and annealed aluminum
I. Hashimoto ‘, J. Mitani a, Y. Miyazaki ‘, H. Yamaguchi ‘, E. Yagi b and M. Iwaki b a Department of Physics, Faculty of Science, Science Universiry of Tokyo, Shinjuku-ku, Tokyo 162, Japan ’ The Institute of Physical and Chemical Research, Wako-shi, Saitama 351-01, Japan
Received 4 December 1992; accepted 30 April 1993
Thin Al foils are implanted with 50 keV Kr ions at room temperature to a dose of 1 X 10’” Kr+ ions/cm’. Kr bubbles in an as-implanted specimen and also in an annealed specimen at 673 K have been examined for 10 mitt by transmission electron microscopy at temperatures between 140 and 300 K. A b&modal size distribution is observed in the annealed specimen, while a single-size distribution is observed in the as-implanted specimen. The lattice parameter of solid fee Kr in the as-implanted specimen is almost constant during cooling, whereas in the annealed one it increases gradually during cooling down to about 190 K and then becomes nearly constant. These parameters are briefly discussed from the view point of the phase transition of highly pressurized Kr.
1. Introduction Rare gas atoms implanted in metals have a low solubility [ll and precipitate into microclusters 12-41. The precipitates are often referred to as bubbles. From the analysis of Ronchi [S], the pressure in the bubbles has been estimated to be of the order of several GPa. Therefore, the bubbles formed by relatively heavy rare gases such as Ar, Kr and Xe are believed to precipitate as a crystalline solid and are aligned epitaxially with fee in an fee host metal at room temperature [6-S]. By in-situ heating experiments in an electron microscope, the melting of the bubbles during heating and the solidification in epitaxial regrowth during cooling have been observed [4,9-l 11. In the specimen ion-implanted at temperatures of 673 K or higher, the precipitation of Kr atoms injected in Ni evolves into a bi-modal size distribution containing small solid precipitates and an additional population of larger, faceted bubbles [12,13]. It is suggested that the swelling in these high gas production rate experiments is primarily controlled by a gas-driven mechanism and that the solid precipitates are immobile, while the larger bubbles move by surface diffusion during the implantation. In contrast with the above mentioned higher temperature injection experiment, Andersen et al. 1141 have carried out an X-ray diffraction experiment on 0022-3115/93/$06.00
cooling of Al single crystals implanted with Kr ions at room temperature. They have suggested to be a bimodal size distribution of bubbles in an annealed specimen up to 620 K and subsequently cooled to 12 K. They have also shown that the larger bubbles estimated to be 9 nm in average size melt at temperatures from 114 to 118 K, whereas smaller bubbles of 3.5 nm remain solids up to 600 K. However, up to the present, the detailed examination by TEM on the size distribution of Kr bubbles in Al has not been carried out yet. In this paper, we will check the state and the size distribution of Kr bubbles both in as-implanted and annealed specimens by means of TEM, and the growth of bubbles during annealing will be discussed. Furthermore, the recrystallization of Kr atoms during cooling will be discussed in terms of the electron diffraction.
2. Experimental procedure Thin Al single crystals were prepared by the strain annealing method from 5-N Al ingots. They were polished by the usual chemical and electrolytical thinning methods [81. The thin foils were implanted with 50 keV at room temperature in vacuum less than 1 x 10e6 Torr to a fluence of 1 x lOi Kr+ ions/cm2. The implantation of Kr ions was carried out by using a Riken low-current implanter with a flux of 1.7 x 10”
0 1993 - Elsevier Science Publishers B.V. All rights reserved
270
I. H~shi~o~o et al. / Rec~sialliza~ion of Kr in Al
Kr+ ions/cm2 s focusing on the target area of 3.3 X 3.3 cm*. This is sufficient to make a dense distribution of solid Kr bubbles. In general, the bright field images of the electron microscopy are used to the direct observation of lattice defects in crystals, while the dark field ones, if the extra electron diffraction reflections from the precipitate in crystals are obtained, have been used to know the distributions of the crystalline precipitates [9]. In our case, if larger bubbles are melting and smaller ones keep solid at room temperature, the size distribution of liquid and solid bubbles both in as-implanted and annealed specimens can be examined directly in comparison with the bright and dark field images taken by the reflection from the solid precipitates. So, at first, we took the bright and dark field images of Kr bubbles in both as-implanted foils and those after annealing at 673 K for 10 mm outside the electron microscope. The latter image was taken by using
the Kr (002) diffracted beams from Kr atoms. The diameter and the density of Kr bubbles were estimated from those images. The cooling experiment for two kinds of specimens was carried out. One was as-implanted and the other was annealed at 673 K for 10 min in vacuum after implantation. Those specimens were observed with a Hitachi H-800 transmission electron microscope attached with a cooling stage of liquid nitrogen operating at 100 kV. The specimens were set to the (100) directions by controlling its orientation and the diffraction reflections observed continuously throughout the cooling experiment. The temperature range was 140-300 K and the intensities of reflections were measured by a microdensitometer. The lattice parameter of Kr was measured from electron diffraction patterns by the simple ratio method [4] between (002) reflections and/or its systematic reflections from Al and Kr atoms. Here the lattice parameter of Al was nearly constant
Fig. 1. Typical electron micrographs of Kr bubbles. Here, (a) and (b) respectively show the bright field image and dark field one taken by the (002) reflection from Kr atoms in an as-implanted specimen. Cc) and Cd) are similar ones using the specimen after annealing at 673 K for 10 min, respectively.
271
I. Hashimotoet al. / Recrystallization of Kr in Al
2
4
6 RO Bubble D ismster
2
4
6
8
[Iml
Fig. 2. Size distributions of Kr bubbles. Here, the opened and the oblique-lined areas represent the relations between the number of bubbles estimated from the bright or the dark field images and their diameter, respectively, and the cross-hatched area is the overlapping part in both images. (a) In the as-implanted state, (b) after annealing at 673 K for 10 min.
during cooling and then the lattice parameter of Kr was determined in comparison with the lattice parameter of Al, a, = 0.4049 nm.
3. Experimental results
as in liquid or gas bubbles during their formation process. On the other hand, the size distributions in the bright and the dark field images of the specimen after annealing at 673 K for 10 min are shown in fig. 2b. Each of the distribution is separated. The mean diameter of smaller bubbles is 2.5 nm, which is the same value as that of the as-implanted one. Combining the bright field image with the dark field one, a b&modal size distribution is obtained where the bubbles larger than 4 nm in diameter are not observed in the dark field images. This shows that the critical size of liquid-solid phase transition of Kr bubbles is around 4 nm in diameter. The total density of Kr bubbles in the bright field image is 1.81 X 10’2/cm2 and the dark field one is 2.05 X 1012/cm2. The overlapped number of Kr bubbles shown by the cross-hatched area in fig. 2b is 2.07 x lO”/cm’. The density of Kr bubbles observed in the as-implanted specimen is 3.14 x 10*2/cm2 as mentioned before and that in the annealed one is 3.65 X 10r2/cmZ and then the density of bubbles increases during annealing. It is noted that a bi-modal size distribution with two maxima at 2.4 and 4.4 nm in diameter is observed in the annealed specimen, whereas there is a single size distribution in the as-implanted specimen. 3.2. Electron di~ruc~i~~
Fig. 1 shows the typical electron micrographs of Kr bubbles. Here, (a)-(d) are the same area, (a) and (b) show the bright field image and the dark field one taken by the (002) reflection from Kr atoms in an as-implanted specimen and (cl and (d) in the specimen after the annealing, respectively. The size distribution of solid Kr bubbles in the specimen from the dark field images taken by the (002) reflection of Kr atoms are shown in fig. 2. Here, opened and oblique-lined areas in the bar graphs show the number of bubbles and their diameter estimated from the bright or the dark field images, respectively, and the cross-hatched area is overlapped ones. The fairly sharp continuous size distribution around the mean diameter of Kr bubbles observed in the bright field image in an as-implanted specimen is nearly the same as that in the dark field image as shown in fig. 2a. The projected densities and the mean diameters are 3.14 X lO’*/cm*, 2.6 nm and 2.26 x 10’z/cm2, 2.5 nm, respectively. We note here that the number of Kr bubbles less than 2.6 nm in diameter is almost the same as in bright and dark field images, while the number of larger one decreases more than 45%. The fact shows that at least a part of these Iarger bubbles more than 2.6 nm in diameter is existing
The cooling experiment of Kr bubbles is carried out in the transmission electron microscope attached with a cooling stage of liquid nitrogen at the temperature ranging from 140 to 300 IL Fig. 3 shows the microdensitometric intensity around (002) diffraction spots of Al for the specimen after annealing at 673 K for 10 min. Here, the curves 1, 2 and 3 show the intensities at
-.270 _______ 197 K I( 139 K
I
Kr
Fig. 3. The microdensitometric intensity distribution around the (002) diffraction spot of Al.
212
I. Hashimotoet al. / Recrystallization of Kr in Al
l
as-implanted
The lattice parameter in an as-implanted specimen is almost constant during cooling down to 140 K as shown in fig. 4. The fact shows that the recrystallization of bubbles in the liquid or gas state in an as-implanted specimen is unexpected to occur during cooling. 4.2. Annealed specimen
Temperature
[Kl
Fig. 4. A change in lattice parameter of Kr during cooling. The lines are drawn only as a guide to the eyes.
278, 197 and 139 K, respectively. The small peak from
Kr atoms is observed apart from the Al (002) spot in the figure. This shows that the Kr atoms precipitate to have an fee lattice epitaxially aligned with the host Al matrix. It is noted here that the intensity of the (002) Kr diffraction reflection increases drastically by cooling the specimen and the integrated intensity ratio is estimated to be 1139/1278= 2.9. This shows that the number of solid Kr bubbles increases during cooling. In this case, the peak position moves towards the center of diffraction reflections (the left hand side), reflecting an increase in the lattice parameter. This is consistent with the result described below. The lattice parameter change during the cooling experiment is shown in fig. 4. Here, solid and open circles show the lattice parameters in an as-implanted specimen and in the annealed one, respectively. The lattice parameter of 0.551 nm is constant in an as-implanted specimen, while in the annealed one, it changes from 0.560 to 0.571 nm during the cooling from 300 to 190 K and becomes almost constant less than 190 K. This shows that the Kr bubbles in a solid phase are constant in an as-implanted specimen, whereas in an annealed one, some of the bubbles would be recrystallized into a solid phase with lowering the temperature depending on the bubble size. The results will be discussed in the next section.
4. Discussions 4.1. As-implanted specimen
As already shown in fig. 2a, almost all bubbles less than 2.6 nm in diameter are in solid, while larger bubbles are in solid by about 55% and then the remaining part is existing as in the liquid or gas state.
Fig. 5 shows the phase diagram of Kr calculated by the empirical Simon’s equation modified by Hardy et al. [15-171. The equation is P=A(T-
7’,,)C-B,
(1)
where P is the melting pressure at the absolute temperature T. A, B, C and T,, are constants and T, = 38.096 (K), A = 3.36253 X low4 (GPa), B = 0.177871 (GPa) and C = 1.44084 for Kr, respectively. The solid line shows the melting curve and the upper part of the line is a solid phase and the lower one is a liquid phase. The dotted lines are the isochore lines and show the relation between pressure and temperature estimated by the analysis of Ronchi [5] as a parameter of the molar volume (cm3/mol in unit) which is shown in the figure. Now, let us consider the relation between diameter and phase transition of Kr bubbles. According to the experimental results as shown in figs. 2a and 4, we assume here that the lattice parameter of Kr is initially equal to 0.551 nm (the molar volume I/ = 25.2 cm3/mol) and that the diameters of bubbles are 2.6 nm. If the molar volume of Kr changes only by the absorption of
100
200 Temperature
300
4 0 Kl
Fig. 5. The phase diagram of Kr atoms calculated by the empirical Simon’s equation modified by Hardy et al. [16]. The solid line shows the melting curve and the upper part of the line is the solid phase and the lower one is the liquid phase. The dotted lines are the isochore lines and are explained in the text. The numbers in the figure indicate the molar volume of Kr atoms and have cm3/mol in unit.
I. Hashimoto et al. / Recrystallization of Kr in Al
vacancies during annealing to the values as shown in fig. 5, the diameters of bubbles will change to 2.7, 2.8 and 2.9 nm in diameter, respectively. Here, the volume change on melting [15] is ignored. The diagram can give us the following conclusions. (A) Seeing a calculated line of 25.2 cm3/mol (2.6 nm in diameter), it is found that Kr bubbles are to be a solid phase at temperatures between 140-300 K. This is confirmed by the observation of as-implanted specimens. That is: (i) Almost all Kr bubbles around 2.6 nm in diameter can be observed on both bright and dark field images (fig. 2a). (ii) The lattice parameter is nearly constant independent of the cooling temperature (fig. 4). (B) If the number of Kr atoms in the bubble keeps constant, the solid Kr bubbles will easily be melting by the growth of only 0.2 nm or so in diameter by absorbing excess vacancies during annealing. For example, when the solid bubbles having 2.6 nm in diameter grow up to 2.8 nm, the molar volume changes to 31.4 cm3/mol and those grown-up bubbles are in liquid at room temperature. Non-conservation of the density of bubbles between as-implanted and annealed specimens as mentioned in section 3.1. is considered as follows. In our early experiment [18], we have observed electron diffraction patterns and electron micrographs obtained at room temperature on the 1 X 1015 Kr+ ions/cm* implanted specimen after annealing at 683 K for 30 min. It was shown that small bubbles were grown during annealing and a bi-modal size distribution appeared. If non-observable small bubbles in an as-implanted specimen are grown by absorbing vacancies during annealing, they become observable so as to increase bubble density. The integrated intensity of diffraction reflections from the Kr+ atoms as shown in fig. 3 increases during cooling. The value at 139 K is stronger by about 3 times than that of the room temperature. Since the integrated intensity of diffraction reflections is proportional to the cube of the number of Kr atoms [19], if the bubbles have the same molar volume and if all the bubbles up to around 4.0 nm in diameter observed in the bright field image shown in fig. 2b are recrystallized during cooling, the increment of the above diffraction reflections can be explained. In this case, the effect of the Debye-Wailer factor is ignored, because of a small value less than 1% [20]. The lattice parameter of the annealed specimen is increased about 0.01 nm during cooling from 300 to 190 K as shown in fig. 4. This is responsible for the recrystallization of bubbles up to around 4 nm in diameter in fig. 2b.
273
Rest and Birtcher [13] have carried out a rate theory approach to interpret observations on the precipitation of Kr, Xe and Ar injected into Ni at temperatures between 398 and 833 K. At temperatures of 673 K or higher, the implanted Kr bubbles evolve into a bi-modal size distribution containing small solid bubbles and an additional population of larger, faceted bubbles. The calculation explores the dependence of the Kr bi-modal size distribution on the maximum size of the solid Kr bubbles and on the bubble mobility. They have suggested that the solid Kr bubbles less than 4 nm in diameter are immobile during high temperature implantation at 773 K in Ni. From our experimental results shown in figs. 2a and 2b, the diameter of moving bubble can be considered to be 3-4 nm, because the density of bubbles larger than these sizes in the bright field images increases after annealing. A part of bubbles larger than 4 nm in diameter is made by the coalescence of 3-4 nm bubbles. When the coalesced bubbles are in solid during cooling, the lattice parameters of Kr are increased with their diameters, because of the difference in the equilibrium pressure before and after the coalescence. Since the solid bubbles of various sizes are distributed in the specimen, the lattice parameter may continuously increase during cooling and the intensity of diffraction spot contrasts is also increased during cooling. In the annealed specimen as shown in fig. 2b, the dark field images do not show the solid bubbles larger than 4 nm. On the other hand, the larger bubbles obtained by Andersen et al. [14] (their estimation is 9 nm in size) melt at temperatures from 114 to 118 K. This is near by the triple point temperature for Kr, 115.763 K. Similar calculations as shown in fig. 5 show again that the melting temperature of bubbles larger than 4 nm in diameter does not depend strongly on their sizes and almost all bubbles of any sizes larger than 4 nm in diameter observed in fig. 2b could be considered to melt at around 115 K. These facts suggest that the heterogeneous growth may occur during annealing by reflecting the heterogeneous density distributions in the specimen and the fairly wide range size distributions may be formed by the annealing.
5. Conclusions (1) From the results obtained by TEM observation of as-implanted foils at room temperature, it follows that almost all bubbles less than 2.6 nm in diameter are solid, while those of larger ones are coexisting in the liquid and the solid phase.
I. Hashimoto et al. / Recrystallization of Kr in AI
214
(2) In the foils annealed at 673 K for 10 min, from the changes of Kr lattice parameter and the integrated intensity of diffraction reflections with cooling temperature, the recrystallization occurs from an early stage of the cooling. (3) The bi-modal size distribution of Kr bubbles constructed with the solid and liquid or gas phases could be clearly observed by TEM.
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