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Molecular dynamics simulation of a swift ion track in NiAl
Nuclear Instruments and Methods in Physics Research B 225 (2004) 97–104 www.elsevier.com/locate/nimb
Molecular dynamics simulation of a swift ion track in NiAl C. Abromeit a
a,*
, A.R. Kuznetsov
b
Hahn-Meitner-Institut Berlin GmbH, Glienicker Str. 100, D-14109 Berlin, Germany b Institute of Metal Physics UD RAS, 620219 Yekaterinburg, Russia Received 13 January 2004; received in revised form 14 April 2004
Abstract The phase transformations in a stoichiometric and non-stoichiometric NiAl alloy under irradiation are theoretically investigated by molecular dynamics (MD) simulation technique with many-body interatomic potentials. The kinetics of the transition of an initially B2 or bcc lattice structure is modelled under thermal conditions and under the influence of a thermal heat spike originating from the slowing down of a swift ion. The results are discussed with respect to lattice changes by projection of the lattice position and with respect to the order-disorder changes by means of a radial distribution function. It is shown that the spike induced a liquid-like structure. For the non-stoichiometric Ni62 Al38 alloy the B2–L10 martensitic transition could be verified. The equilibrium (martensitic L10 ) phase cannot be reached in ion tracks on the first stage, when diffusion in a solid does not play a role. Sine-like lattice oscillations are transformed into a sequence of kink-like excitations – ‘‘soliton lattice’’. The character of formed domain structure and the kinetics of the transition depends on the presence of a track. 2004 Elsevier B.V. All rights reserved. PACS: 02.70.Uu; 61.80Jh; 61.82.Bg; 64.70.Kb Keywords: Molecular dynamics; Ion tracks; Phase transformation; NiAl; Thermal spike
1. Introduction The structural and chemical transformation induced by irradiation of alloys with energetic ions can change the physical properties of the materials drastically. Especially the diffusionless austenite– martensite phase transformation is very sensitive to the applied irradiation parameters [1,2]. For low energy ions the slowing down of the ions is mainly
*
Corresponding author. Tel.: +49-30-8062-2825; fax: +4930-8062-3059. E-mail address: [email protected] (C. Abromeit).
determined by nuclear stopping. Extended defect structures i.e. point defects, defect clusters and disordered zones in ordered structures are produced by the direct atom–atom interaction in replacement collisions. In the high energy regime (Z P 40 and ion energies between 1 and 10 MeV/ u), however, the ions loose energy mainly by electronic interaction. The cylindrical energy deposition into the electronic system can form tracks. The details of the track-formation mechanism are currently investigated by several groups theoretically and experimentally [3]. The extremely strong electronic excitations inside a track can result in a significant
0168-583X/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.04.181
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modification of the solid-state structure, e.g. martensitic phase transformations are possible (see the review about martensitic transformations in [4]) and order–disorder transformations in ordered alloys [2]). Examples for such transformation are Ni–Al and Ni–Ti alloys where martensitic transformations are well documented (experimental details can be found in [5]). In this study we chose stoichiometric and non-stoichiometric NiAl which undergoes a B2–L10 martensitic transition, order– disorder transition and also amorphization under irradiation. For NiAl the many-body interatomic potentials are sufficiently known to apply the molecular dynamics method for the simulation of the phase transformation [6,7]. This method is suitable for a study of such a fast process as track formation and to simulate at the atomic level the process of the track formation and possible transitions.
ordered alloys the atoms were distributed statistically. In the first stage the local heating of the lattice inside an ion track was simulated. Layers with thickness approx. 0.5 nm near the XZ, YZ boundaries of the crystallite, which are parallel to the
2. Computational procedure During the simulation we used many-body interatomic potentials based on the embedded atom method (EAM) developed by Voter and Chen [8]. The potentials were successfully applied to simulations of the B2 fi L10 martensitic transition in NiAl crystallite by the group of Clapp [9]. A cubic crystallite with initial B2 structure (½0 0 1, ½0 1 0 and ½1 0 0 directions parallel to the X -, Y - and Zaxis) was chosen (approximately 4.6 · 4.6 · 4.6 nm and 8000 atoms). It is large enough to have a volume for heating of a substantial size inside. The irradiation experiments on NiTi [2] and evaluations of spike diameters for metals [10] showed, that the diameter of a melted region in a track ranges from several nm till approximately 10 nm. In our calculations a cylindrically heated volume of 1 nm diameter and a length 4.6 nm along the Zaxis was used. The MD time step was 1 and 2 fs. The temperature control was performed by means of rescaling of the velocities. The simulation was performed at constant volume with periodic boundary conditions (sometimes part of the crystallite surfaces were left free; constant pressure simulation was also performed using Andersen’s Method [11]). In the non-stoichiometric and dis-
Fig. 1. Structures of initially ordered Ni50 Al50 alloy with track: (a) track heating at 5000 K, after 8 ps; (b) annealing at 100 K, after 0.8 ps; (c) annealing at 100 K, after 80 ps.
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Fig. 2. RDF for initially ordered B2 Ni50 Al50 alloy: (a) after track heating at 5000 K during 8 ps; (b) for liquid state (for comparison); (c) after annealing at 100 K during 80 ps; (d) for ordered B2 alloy, 100 K (for comparison).
Fig. 3. Structures and RDF for initially ordered Ni62 Al38 alloy without track: (a) annealing at 100 K, after 0.8 ps; (b) after 4 ps; (c) after 80 ps; (d) RDF after 80 ps, corresponds to the structure on ‘‘c’’; (e) RDF for ordered L10 Ni62 Al38 alloy, 100 K, equilibrium phase (for comparison).
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track, were kept at temperature TB ¼ 100 K. A constant track temperature TT ¼ 5000 K was imposed on the atoms inside the heated volume. This temperature is substantially higher than the melting temperature of NiAl. It corresponds to the temperatures which were determined from the MD simulation of a disordering kinetics in NiAl under ion irradiation in a displacement cascade [12]. The track temperature was kept constant up to 8000 MD steps of 2 ps (but commonly 4000 steps or 8 ps). This time is long enough that the energy, deposited in the electronic system in the track, is transferred to the atoms with a characteristic time of the order of 1012 s [10]. Also we used longer heating times than 1 ps because it could help to check the possibility of an amorphization of the alloy induced by the swift ion tracks. On the second stage crystallization was simulated by two different quenching rates. In the first simulation run the whole crystallite was instantaneously quenched to 100 K and annealed at this temperature up to 40 000 steps. At this temperature a B2 fi L10 martensitic transition (TC 300 K) had been observed in MD simulations of NiAl [9]. In the second simulation run only the heating inside the track had been stopped after spike production (after heating during 8 ps). In this case the temperature in the sample decays according to the heat conduction law approaching the boundary temperature T ¼ 100 K. The conditions of the second simulation run are less favorable for the amorphization of the track. They are often used in collision cascade simulations. Here they were utilized for a comparison. In addition to the lattice positions the radial distribution functions (RDF) nðrÞ were calculated (including for Ni–Ni, Ni–Al and Al–Al atoms), where nðrÞ is the average number of particles located at the distances r; . . . ; r þ Dr from the given particle; Dr is a small value compared with r. They are shown in the next section.
stage of the simulation – heating of the track. We see, that all volume of the track is melted after 8 ps. The melting of the track is confirmed by the comparison of the RDF (Fig. 2(a)) with the shape of the RDF for the liquid alloy (compare with Fig. 2(b), where the RDF for a melted sample is given). Both RDF show the same behaviour. Figs. 1(b) and (c) show the second stage of the simulation – annealing (recovery) of the crystallite with melted track at the low temperature T ¼ 100 K, which is below the TC of the martensitic transition. It can be seen, that after 20 ps of annealing at the low temperature the alloy in the track has been crystallized in BCC-type structure (see RDF on Fig. 2(c)), although the structure is not perfect. We compare this RDF with the RDF for perfect B2 ordered Ni50 Al50 alloy (Fig. 2(d)) and notice that an alloy in the track after the crystallization is
3. Results and discussion First we consider initially B2 ordered Ni50 Al50 alloy. Fig. 1(a) shows XY projections of the crystallite (perpendicular to the track) after the first
Fig. 4. Structures and RDF for initially ordered B2 Ni62 Al38 alloy with track: (a) track heating at 5000 K, after 1.6 ps; (b) after 8 ps.
C. Abromeit, A.R. Kuznetsov / Nucl. Instr. and Meth. in Phys. Res. B 225 (2004) 97–104
disordered. Thus it can be stated, that there was disordering in the track, but no martensitic transition. It is known from experimental data [5] that Ni1x Alx alloys are exhibiting martensitic transformation B2–L10 in the concentration range 34 at.% < x < 40 at.%. Therefore we chose Ni62 Al38 alloy to study the transition. In order to prove the used potentials we simulated initially ordered alloy without track. Fig. 3 shows the kinetics of the transition. The evolution during the transition seems to be the same as in [9,13]. In this case we got domains of close packed martensitic structure. The next figures show the results of an initially ordered Ni62 Al38 alloy with a formation of a track. Fig. 4 shows heating stage, Figs. 5 and 6 – annealing at 100 K after different quenching rates. The alloy melts in the track after heating stage (see relevant RDF) and exhibits the martensitic transition during annealing with formation of the domain structure similar to the structure in the previous case. The details of the domain structure, however, depend on the quenching rate (Figs. 5 and 6). Most likely, the alloy in the track is dis-
101
ordered (the RDF is similar to RDF on Fig. 2(a)). Thus, the material in the track has undergone an order–disorder and a structural transition. It seems interesting to study initially disordered Ni62 Al38 alloy also. Experimentally it can be prepared by irradiation of ordered one. Our simulation showed, that for this alloy the martensitic transition TC is between 1200 and 1500 K. Fig. 7 shows kinetics of the martensitic transition in the alloy without track, annealed at 100 K. Visually the final domain structure of the martensitic phase is similar to the structure of martensitic phase for initially ordered Ni62 Al38 alloy. Fig. 8 shows kinetics of the martensitic transition with a track, heated and annealed at 100 K. As soon as the driving force of the BCC fi ‘‘close packed structure’’ martensitic transition (BCC is stable at high temperature) is higher (because TC is high), the martensitic transition happened even during the heating stage. During the annealing stage the track was crystallized already in the martensitic phase. The final domain structure differs from the final martensitic structures obtained in other cases.
Fig. 5. Annealing behaviour of an initially ordered B2 Ni62 Al38 alloy with track after an instantaneously quench to 100 K: (a), (b) and (c) structure after annealing at 100 K, after 0.8, 4 and 80 ps, correspondingly; (d) RDF after 80 ps, corresponds to the structure on ‘‘c’’; (e) RDF for disordered FCC Ni62 Al38 alloy, 100 K (for comparison).
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Fig. 6. Structure and RDF of an initially ordered B2 Ni62 Al38 alloy with track after an diffusion-controlled temperature decay to 100 K after 40 ps: (a) 100 projection, (b) RDF.
From our MD simulations it follows that in the case without track (see Figs. 3 and 7) the nucleation of a new martensitic phase is a result of a phonon instability development. The sine-like lattice oscillations, which are seen on Figs. 3(b) and 7(a), are transformed into a sequence of kink-like excitations – ‘‘soliton lattice’’ (Figs. 3(c) and 7(b)). The pre-requisites for the appearance of this instability seems to be the presence of soft branch of transverse phonons in the h1 1 0i direction, this ‘‘softness’’ is characteristic for BCC lattice, e.g. it was seen in simulations of BCC fi HCP transition in Zr [14,15]. In the case of the martensitic transition in the presence of a swift ion track, the transition mechanism can be changed. A track destroys the crystal structure (melts it), that prevents from developing of one long-wavelength instability. It seems that in this case the new phase nucleates in
Fig. 7. Structures and RDF for initially disordered BCC Ni62 Al38 alloy without track: (a) annealing at 100 K, after 2.4 ps; (b) after 80 ps; (c) RDF after 80 ps, corresponds to the structure on ‘‘b’’.
several places simultaneously near the track. The final domain structure differs. Further work on more detailed analysis of final structure and mechanism of the martensitic transition is in progress.
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Fig. 8. Structures and RDF for initially disordered BCC Ni62 Al38 alloy with track: (a), (b) and (c) – track heating at 5000 K, after 1.6, 2.4 and 8 ps, correspondingly; (d)–(f) annealing at 100 K, after 0.8, 2.4 and 80 ps, correspondingly; (g) RDF for track heating after 8 ps, corresponds to the structure of the track on ‘‘c’’; (h) RDF for annealing after 80 ps, corresponds to the structure of the track on ‘‘f’’.
4. Conclusion We have shown that swift ions form tracks in NiAl and induce the following microstructural modifications: melting and crystallization, orderdisorder and martensitic transformations. Disordering, induced in the track, is kept after its crystallization. Equilibrium (martensitic L10 ) phase cannot be reached in ion tracks on the first stage, when diffusion in a solid does not play a role. Martensitic transition commonly begins from the development of lattice instability. The sine-like lattice oscillations are transformed into a sequence of kink-like excitations – ‘‘soliton lat-
tice’’. The character of formed domain structure and the kinetics of the transition can depend on the presence of a track and on the quenching rate. A track can change the scheme of the martensitic transition, i.e. it can be started near the track without freezing of one long-wavelength phonon.
Acknowledgements Part of this work had been funded by the HGF Strategiefond Projekt ‘‘Ion Tracks in Solids’’ at the Hahn-Meitner-Institut Berlin.
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References [1] D.S. Grummon, R. Gotthardt, Acta Mater. 48 (2000) 635. [2] A. Barbu, A. Dunlop, A. Hardouin Duparc, G. Jaskierowiscz, N. Lorenzelli, Nucl. Instr. and Meth. B 145 (1998) 354. [3] SHIM 2002 Conference (Sicilia), Nucl. Instr. and Meth. B 209 (2003). [4] L. Delaey, Diffusionless transformations, in: P. Haasen (Ed.), Materials Science and Technology, VCH, Weinheim, 1991, p. 5. [5] D. Schryvers, J. Phys. (Paris) IV C2 (1995) 225. [6] S. Rubini, P. Ballone, Phys. Rev. B 48 (1993) 99.
[7] S. Rubini, Thesis EPFL Lausanne, No. 1095, 1992. [8] A.F. Voter, S.P. Chen, MRS Proc. 82 (1987) 175. [9] Y. Shao, P.C. Clapp, J.R. Rifkin, Metall. Mater. Trans. 27A (1996) 1489. [10] M. Toulemonde, C. Dufour, E. Paumier, Phys. Rev. B 46 (1992) 14362. [11] H.C. Andersen, J. Chem. Phys. 72 (4) (1980). [12] M. Spaczer, A. Caro, M. Victoria, T. Diaz de la Rubia, Phys. Rev. B 50 (1994) 13204. [13] R. Meyer, P. Entel, Comp. Mater. Sci. 10 (1998) 10. [14] J.R. Morris, K.M. Ho, Phys. Rev. B 63 (2001) 224116. [15] A.R. Kuznetsov, Yu.N. Gornostyrev, M.I. Katsnelson, A.V. Trefilov, Mater. Sci. Eng. A 309–310 (2001) 168.
Molecular dynamics simulation of a swift ion track in NiAl C. Abromeit a
a,*
, A.R. Kuznetsov
b
Hahn-Meitner-Institut Berlin GmbH, Glienicker Str. 100, D-14109 Berlin, Germany b Institute of Metal Physics UD RAS, 620219 Yekaterinburg, Russia Received 13 January 2004; received in revised form 14 April 2004
Abstract The phase transformations in a stoichiometric and non-stoichiometric NiAl alloy under irradiation are theoretically investigated by molecular dynamics (MD) simulation technique with many-body interatomic potentials. The kinetics of the transition of an initially B2 or bcc lattice structure is modelled under thermal conditions and under the influence of a thermal heat spike originating from the slowing down of a swift ion. The results are discussed with respect to lattice changes by projection of the lattice position and with respect to the order-disorder changes by means of a radial distribution function. It is shown that the spike induced a liquid-like structure. For the non-stoichiometric Ni62 Al38 alloy the B2–L10 martensitic transition could be verified. The equilibrium (martensitic L10 ) phase cannot be reached in ion tracks on the first stage, when diffusion in a solid does not play a role. Sine-like lattice oscillations are transformed into a sequence of kink-like excitations – ‘‘soliton lattice’’. The character of formed domain structure and the kinetics of the transition depends on the presence of a track. 2004 Elsevier B.V. All rights reserved. PACS: 02.70.Uu; 61.80Jh; 61.82.Bg; 64.70.Kb Keywords: Molecular dynamics; Ion tracks; Phase transformation; NiAl; Thermal spike
1. Introduction The structural and chemical transformation induced by irradiation of alloys with energetic ions can change the physical properties of the materials drastically. Especially the diffusionless austenite– martensite phase transformation is very sensitive to the applied irradiation parameters [1,2]. For low energy ions the slowing down of the ions is mainly
*
Corresponding author. Tel.: +49-30-8062-2825; fax: +4930-8062-3059. E-mail address: [email protected] (C. Abromeit).
determined by nuclear stopping. Extended defect structures i.e. point defects, defect clusters and disordered zones in ordered structures are produced by the direct atom–atom interaction in replacement collisions. In the high energy regime (Z P 40 and ion energies between 1 and 10 MeV/ u), however, the ions loose energy mainly by electronic interaction. The cylindrical energy deposition into the electronic system can form tracks. The details of the track-formation mechanism are currently investigated by several groups theoretically and experimentally [3]. The extremely strong electronic excitations inside a track can result in a significant
0168-583X/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2004.04.181
98
C. Abromeit, A.R. Kuznetsov / Nucl. Instr. and Meth. in Phys. Res. B 225 (2004) 97–104
modification of the solid-state structure, e.g. martensitic phase transformations are possible (see the review about martensitic transformations in [4]) and order–disorder transformations in ordered alloys [2]). Examples for such transformation are Ni–Al and Ni–Ti alloys where martensitic transformations are well documented (experimental details can be found in [5]). In this study we chose stoichiometric and non-stoichiometric NiAl which undergoes a B2–L10 martensitic transition, order– disorder transition and also amorphization under irradiation. For NiAl the many-body interatomic potentials are sufficiently known to apply the molecular dynamics method for the simulation of the phase transformation [6,7]. This method is suitable for a study of such a fast process as track formation and to simulate at the atomic level the process of the track formation and possible transitions.
ordered alloys the atoms were distributed statistically. In the first stage the local heating of the lattice inside an ion track was simulated. Layers with thickness approx. 0.5 nm near the XZ, YZ boundaries of the crystallite, which are parallel to the
2. Computational procedure During the simulation we used many-body interatomic potentials based on the embedded atom method (EAM) developed by Voter and Chen [8]. The potentials were successfully applied to simulations of the B2 fi L10 martensitic transition in NiAl crystallite by the group of Clapp [9]. A cubic crystallite with initial B2 structure (½0 0 1, ½0 1 0 and ½1 0 0 directions parallel to the X -, Y - and Zaxis) was chosen (approximately 4.6 · 4.6 · 4.6 nm and 8000 atoms). It is large enough to have a volume for heating of a substantial size inside. The irradiation experiments on NiTi [2] and evaluations of spike diameters for metals [10] showed, that the diameter of a melted region in a track ranges from several nm till approximately 10 nm. In our calculations a cylindrically heated volume of 1 nm diameter and a length 4.6 nm along the Zaxis was used. The MD time step was 1 and 2 fs. The temperature control was performed by means of rescaling of the velocities. The simulation was performed at constant volume with periodic boundary conditions (sometimes part of the crystallite surfaces were left free; constant pressure simulation was also performed using Andersen’s Method [11]). In the non-stoichiometric and dis-
Fig. 1. Structures of initially ordered Ni50 Al50 alloy with track: (a) track heating at 5000 K, after 8 ps; (b) annealing at 100 K, after 0.8 ps; (c) annealing at 100 K, after 80 ps.
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Fig. 2. RDF for initially ordered B2 Ni50 Al50 alloy: (a) after track heating at 5000 K during 8 ps; (b) for liquid state (for comparison); (c) after annealing at 100 K during 80 ps; (d) for ordered B2 alloy, 100 K (for comparison).
Fig. 3. Structures and RDF for initially ordered Ni62 Al38 alloy without track: (a) annealing at 100 K, after 0.8 ps; (b) after 4 ps; (c) after 80 ps; (d) RDF after 80 ps, corresponds to the structure on ‘‘c’’; (e) RDF for ordered L10 Ni62 Al38 alloy, 100 K, equilibrium phase (for comparison).
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track, were kept at temperature TB ¼ 100 K. A constant track temperature TT ¼ 5000 K was imposed on the atoms inside the heated volume. This temperature is substantially higher than the melting temperature of NiAl. It corresponds to the temperatures which were determined from the MD simulation of a disordering kinetics in NiAl under ion irradiation in a displacement cascade [12]. The track temperature was kept constant up to 8000 MD steps of 2 ps (but commonly 4000 steps or 8 ps). This time is long enough that the energy, deposited in the electronic system in the track, is transferred to the atoms with a characteristic time of the order of 1012 s [10]. Also we used longer heating times than 1 ps because it could help to check the possibility of an amorphization of the alloy induced by the swift ion tracks. On the second stage crystallization was simulated by two different quenching rates. In the first simulation run the whole crystallite was instantaneously quenched to 100 K and annealed at this temperature up to 40 000 steps. At this temperature a B2 fi L10 martensitic transition (TC 300 K) had been observed in MD simulations of NiAl [9]. In the second simulation run only the heating inside the track had been stopped after spike production (after heating during 8 ps). In this case the temperature in the sample decays according to the heat conduction law approaching the boundary temperature T ¼ 100 K. The conditions of the second simulation run are less favorable for the amorphization of the track. They are often used in collision cascade simulations. Here they were utilized for a comparison. In addition to the lattice positions the radial distribution functions (RDF) nðrÞ were calculated (including for Ni–Ni, Ni–Al and Al–Al atoms), where nðrÞ is the average number of particles located at the distances r; . . . ; r þ Dr from the given particle; Dr is a small value compared with r. They are shown in the next section.
stage of the simulation – heating of the track. We see, that all volume of the track is melted after 8 ps. The melting of the track is confirmed by the comparison of the RDF (Fig. 2(a)) with the shape of the RDF for the liquid alloy (compare with Fig. 2(b), where the RDF for a melted sample is given). Both RDF show the same behaviour. Figs. 1(b) and (c) show the second stage of the simulation – annealing (recovery) of the crystallite with melted track at the low temperature T ¼ 100 K, which is below the TC of the martensitic transition. It can be seen, that after 20 ps of annealing at the low temperature the alloy in the track has been crystallized in BCC-type structure (see RDF on Fig. 2(c)), although the structure is not perfect. We compare this RDF with the RDF for perfect B2 ordered Ni50 Al50 alloy (Fig. 2(d)) and notice that an alloy in the track after the crystallization is
3. Results and discussion First we consider initially B2 ordered Ni50 Al50 alloy. Fig. 1(a) shows XY projections of the crystallite (perpendicular to the track) after the first
Fig. 4. Structures and RDF for initially ordered B2 Ni62 Al38 alloy with track: (a) track heating at 5000 K, after 1.6 ps; (b) after 8 ps.
C. Abromeit, A.R. Kuznetsov / Nucl. Instr. and Meth. in Phys. Res. B 225 (2004) 97–104
disordered. Thus it can be stated, that there was disordering in the track, but no martensitic transition. It is known from experimental data [5] that Ni1x Alx alloys are exhibiting martensitic transformation B2–L10 in the concentration range 34 at.% < x < 40 at.%. Therefore we chose Ni62 Al38 alloy to study the transition. In order to prove the used potentials we simulated initially ordered alloy without track. Fig. 3 shows the kinetics of the transition. The evolution during the transition seems to be the same as in [9,13]. In this case we got domains of close packed martensitic structure. The next figures show the results of an initially ordered Ni62 Al38 alloy with a formation of a track. Fig. 4 shows heating stage, Figs. 5 and 6 – annealing at 100 K after different quenching rates. The alloy melts in the track after heating stage (see relevant RDF) and exhibits the martensitic transition during annealing with formation of the domain structure similar to the structure in the previous case. The details of the domain structure, however, depend on the quenching rate (Figs. 5 and 6). Most likely, the alloy in the track is dis-
101
ordered (the RDF is similar to RDF on Fig. 2(a)). Thus, the material in the track has undergone an order–disorder and a structural transition. It seems interesting to study initially disordered Ni62 Al38 alloy also. Experimentally it can be prepared by irradiation of ordered one. Our simulation showed, that for this alloy the martensitic transition TC is between 1200 and 1500 K. Fig. 7 shows kinetics of the martensitic transition in the alloy without track, annealed at 100 K. Visually the final domain structure of the martensitic phase is similar to the structure of martensitic phase for initially ordered Ni62 Al38 alloy. Fig. 8 shows kinetics of the martensitic transition with a track, heated and annealed at 100 K. As soon as the driving force of the BCC fi ‘‘close packed structure’’ martensitic transition (BCC is stable at high temperature) is higher (because TC is high), the martensitic transition happened even during the heating stage. During the annealing stage the track was crystallized already in the martensitic phase. The final domain structure differs from the final martensitic structures obtained in other cases.
Fig. 5. Annealing behaviour of an initially ordered B2 Ni62 Al38 alloy with track after an instantaneously quench to 100 K: (a), (b) and (c) structure after annealing at 100 K, after 0.8, 4 and 80 ps, correspondingly; (d) RDF after 80 ps, corresponds to the structure on ‘‘c’’; (e) RDF for disordered FCC Ni62 Al38 alloy, 100 K (for comparison).
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Fig. 6. Structure and RDF of an initially ordered B2 Ni62 Al38 alloy with track after an diffusion-controlled temperature decay to 100 K after 40 ps: (a) 100 projection, (b) RDF.
From our MD simulations it follows that in the case without track (see Figs. 3 and 7) the nucleation of a new martensitic phase is a result of a phonon instability development. The sine-like lattice oscillations, which are seen on Figs. 3(b) and 7(a), are transformed into a sequence of kink-like excitations – ‘‘soliton lattice’’ (Figs. 3(c) and 7(b)). The pre-requisites for the appearance of this instability seems to be the presence of soft branch of transverse phonons in the h1 1 0i direction, this ‘‘softness’’ is characteristic for BCC lattice, e.g. it was seen in simulations of BCC fi HCP transition in Zr [14,15]. In the case of the martensitic transition in the presence of a swift ion track, the transition mechanism can be changed. A track destroys the crystal structure (melts it), that prevents from developing of one long-wavelength instability. It seems that in this case the new phase nucleates in
Fig. 7. Structures and RDF for initially disordered BCC Ni62 Al38 alloy without track: (a) annealing at 100 K, after 2.4 ps; (b) after 80 ps; (c) RDF after 80 ps, corresponds to the structure on ‘‘b’’.
several places simultaneously near the track. The final domain structure differs. Further work on more detailed analysis of final structure and mechanism of the martensitic transition is in progress.
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Fig. 8. Structures and RDF for initially disordered BCC Ni62 Al38 alloy with track: (a), (b) and (c) – track heating at 5000 K, after 1.6, 2.4 and 8 ps, correspondingly; (d)–(f) annealing at 100 K, after 0.8, 2.4 and 80 ps, correspondingly; (g) RDF for track heating after 8 ps, corresponds to the structure of the track on ‘‘c’’; (h) RDF for annealing after 80 ps, corresponds to the structure of the track on ‘‘f’’.
4. Conclusion We have shown that swift ions form tracks in NiAl and induce the following microstructural modifications: melting and crystallization, orderdisorder and martensitic transformations. Disordering, induced in the track, is kept after its crystallization. Equilibrium (martensitic L10 ) phase cannot be reached in ion tracks on the first stage, when diffusion in a solid does not play a role. Martensitic transition commonly begins from the development of lattice instability. The sine-like lattice oscillations are transformed into a sequence of kink-like excitations – ‘‘soliton lat-
tice’’. The character of formed domain structure and the kinetics of the transition can depend on the presence of a track and on the quenching rate. A track can change the scheme of the martensitic transition, i.e. it can be started near the track without freezing of one long-wavelength phonon.
Acknowledgements Part of this work had been funded by the HGF Strategiefond Projekt ‘‘Ion Tracks in Solids’’ at the Hahn-Meitner-Institut Berlin.
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References [1] D.S. Grummon, R. Gotthardt, Acta Mater. 48 (2000) 635. [2] A. Barbu, A. Dunlop, A. Hardouin Duparc, G. Jaskierowiscz, N. Lorenzelli, Nucl. Instr. and Meth. B 145 (1998) 354. [3] SHIM 2002 Conference (Sicilia), Nucl. Instr. and Meth. B 209 (2003). [4] L. Delaey, Diffusionless transformations, in: P. Haasen (Ed.), Materials Science and Technology, VCH, Weinheim, 1991, p. 5. [5] D. Schryvers, J. Phys. (Paris) IV C2 (1995) 225. [6] S. Rubini, P. Ballone, Phys. Rev. B 48 (1993) 99.
[7] S. Rubini, Thesis EPFL Lausanne, No. 1095, 1992. [8] A.F. Voter, S.P. Chen, MRS Proc. 82 (1987) 175. [9] Y. Shao, P.C. Clapp, J.R. Rifkin, Metall. Mater. Trans. 27A (1996) 1489. [10] M. Toulemonde, C. Dufour, E. Paumier, Phys. Rev. B 46 (1992) 14362. [11] H.C. Andersen, J. Chem. Phys. 72 (4) (1980). [12] M. Spaczer, A. Caro, M. Victoria, T. Diaz de la Rubia, Phys. Rev. B 50 (1994) 13204. [13] R. Meyer, P. Entel, Comp. Mater. Sci. 10 (1998) 10. [14] J.R. Morris, K.M. Ho, Phys. Rev. B 63 (2001) 224116. [15] A.R. Kuznetsov, Yu.N. Gornostyrev, M.I. Katsnelson, A.V. Trefilov, Mater. Sci. Eng. A 309–310 (2001) 168.