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Atomic flows, coronas and cratering in Au, Si and SiO2
Nuclear Instruments and Methods in Physics Research B 267 (2009) 1420–1423
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Atomic flows, coronas and cratering in Au, Si and SiO2 Kai Nordlund *, Juha Samela Helsinki Institute of Physics and Department of Physics, University of Helsinki, P.O. Box 43, FI-00014, Finland
a r t i c l e
i n f o
Article history: Available online 3 February 2009 PACS: 79.20. m 61.80.Jh 83.10.Rs Keywords: Cratering Ion impacts Crater impacts Molecular dynamics simulation
a b s t r a c t The traditional picture of ion irradiation effects in materials was that of a series of binary collisions. Since the 1980’s it has, however, become clear that collective many-body effects such as heat spikes and flow of liquid matter can be important in dense metals. Now very recent atomistic simulations indicate that during MeV cluster ion bombardment, the irradiation effects start to resemble macroscopic phenomena such as the splashes and coronas observed when heavy objects fall on water. In this article, we review recent work showing that the craters formed during cluster impacts start to behave like macroscopic cratering beyond a certain impactor size. We also present new results which show that for cluster sizes of only around 100 atoms, not only dense metals, but also brittle materials like Si and SiO2 start to exhibit hydrodynamic-like behaviour of collective atom flow and corona formation. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction For a long time, the theoretical understanding of ion irradiation effects in materials was almost solely based on treating the irradiation process as a series of binary collisions [1]. While this kind of treatment certainly is adequate for a wide range of irradiation conditions, since the 1980’s it has started to become clear that also collective phenomena like formation of hot molten zones of matter and flow of atoms can be important and even dominate the behaviour [2–5]. This development of understanding naturally followed the computer capacity available. Until the 1980’s only computationally efficient binary collision approximation [1] methods were fast enough for practical use in simulation of collision cascades in the heat spike regime. However, when computers became fast enough in the 1990’s to treat many-body collisional effects of tens of thousands of atoms, molecular dynamics (MD) simulations could be used to directly simulate the heat spikes [3,6,4,7], the existence of which had in fact already been predicted in the 1950’s [8]. One intriguing heat spike phenomenon is the formation of craters on surfaces by the impacts of single atoms [2,4,5]. Ever since these were first observed, it was clear that they at least superficially resemble the craters formed on the surfaces of planets and moons by impacting meteoroids and asteroids. However, it has not been clear whether the mechanisms of atomic and macroscopic cratering are really the same, or whether the similarity is * Corresponding author. E-mail address: kai.nordlund@helsinki.fi (K. Nordlund). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.01.125
just coincidental. Some observations have indeed indicated that there must be a clear difference in the mechanisms. The scaling laws applied to macroscopic craters do not match those obtained on the atomic scale [9]. Moreover, for single ion impacts, large craters are observed on the surfaces of metals like Au but not brittle materials like Ge [10,11], even though almost all astronomical craters are of course formed on brittle rock-like materials. Now that computer capacity has advanced further from the 1990’s level, it is possible to simulate systems with tens of millions of atoms for the full duration of a collision cascade and its relaxation phase. This has enabled simulation of ion and cluster ion impacts with impactor energies exceeding well above 1 MeV. Such simulations have shown that in very large collisional systems, the behaviour starts in many ways to resemble purely macroscopic phenomena like flows, splash crown and corona formation and pressure-induced cratering [12–14]. In this article, we review our very recent work on metals that shows how the atomistic cratering transforms into the macroscopic one and present previously unpublished results on splash crowns in Si and SiO2 . 2. Method Ion and cluster ion impacts were simulated with classical molecular dynamics employing many-body interatomic potentials implemented in the PARCAS MD code [15,16]. The basic simulation methodology has been described in several previous works [7,17– 19], so here we only summarize the interaction models used, as this is relevant for understanding the comparison of materials. To simulate Au we used a corrected effective medium (CEM) potential
K. Nordlund, J. Samela / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1420–1423
which has been constructed to describe surfaces and small clusters [20]. It also describes well elasticity and melting of Au and has been found to predict sputtering yields which agree very well with experiments [18]. For Si we have tested a wide range of interatomic potentials and found that while none agrees with all experiments they have been compared against, most of them predict qualitatively similar crater formation and sputtering behaviour [21]. To simulate quartz and silica we employ the Stillinger–Weber-like potential by Watanabe and Samela [22,23]. This potential has the correct ground state of a-quartz, has been shown to describe well the structure of amorphous silica and can describe both pure Si and SiO2 in the same parametrisation [23,24]. For the Ar interactions we used the purely repulsive universal ZBL potential [25]. The projectiles were chosen to be Au (for impacts on Au) or Ar (for impacts on Si and SiO2 ) clusters in the size range 1–316,000 atoms. The shape was spherical or in some cases cubic to test whether the projectile shape affects the results. In all cases the projectiles were first independently relaxed at 300 K with an MD sim-
1421
ulation to ensure that they do not have extra internal energy that could effect the outcome. For the cubic projectiles, this lead to a smoothing of the edges due to surface atom migration.
3. Results and discussion Examination of how the atomic cratering transforms into the macroscopic one is made easier by the fact that the mechanisms of the latter kind are fairly well understood. Macroscopic cratering is usually divided in two regimes, the strength and gravity regimes [26,27]. In the former, the final crater size (for a given projectile and energy) is determined by the strength of the material, while in the latter also gravity plays a role. The gravity regime starts to emerge for impactors with sizes of tens of meters or more and is thus irrelevant in the current context. The strength regime is relevant to small meteoroids, but also projectiles from e.g. gas guns, bullets and micrometeorites [26,28,29].
Fig. 1. Snapshots from MD simulations of corona formation during cluster ion irradiation of Au and Si. The top two frames show bombardment of Au and bottom two of Si. For the Au cases the projectile as Au6800 at an energy of 500 eV/atom, for Si it was Ar147 at an energy of 400 eV/atom.
Fig. 2. Formation of a high-pressure region in (a) 500 eV/atom Au101000 impact on Au and (b) 100 eV/atom Ar100000 impact on SiO2 . The figures are snapshots where the colour (grey) scale shows the local atomic density around the atom divided by the normal equilibrium density. Blue (darker) spheres show normal or low densities and red (lighter) spheres show higher densities. The darkest red corresponds to an atom density of about three times the normal one. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
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K. Nordlund, J. Samela / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1420–1423
In the strength regime, the basic reason to cratering is, based on experiments and hydrodynamic modelling, known to be the formation of a high-pressure region below the impactor [26,30,31]. When the high-pressure is released, a crown is formed, which subsequently breaks up leading to the emission of ejecta and formation of a crater rim. A similar process is known to occur for all kinds of materials, ranging from dense metals to sand, rock and liquids (in which case the crater is of course only transient). To find where the atomistic cratering mechanism transforms into the macroscopic one, we started with the insight that typical meteoroid impacts occur for velocities around 22 km/s, which when translated to kinetic energy means about 500 eV/atom for Au. This is of course, but purely coincidentally, a typical ion beam energy. We thus were able to use our existing ion beam MD codes and methods to systematically simulate bombardment of Au with increasingly large projectiles with a constant energy of 500 eV/ atom [14]. Since the kinetic energy (velocity) corresponds exactly to that of macroscopic impacts, the cratering mechanism presumably should for large enough projectile size transform into the macroscopic one. To obtain a point of comparison in brittle materials, for the current article, we also simulated Ar cluster impacts on Si. Recall that it is known that single atoms form no or only small craters or hillocks (height 0.5 nm or less) in Si or Ge [10,32,23], so appearance of macroscopic-like behaviour must occur for larger projectile sizes. Development of a splash crown and its subsequent breakup is illustrated in Fig. 1 for Au and Ar clusters. Clearly in both Au and Si a macroscopic-like hydrodynamic behaviour is present. To obtain a quantitative measure of whether the cratering mechanism really corresponds to the macroscopic ones, we have carried out several types of analyses of the cratering behaviour [19,12–14]. The most useful ones with respect to finding the transition to macroscopic behaviour have been analysis of the local density of each atom below the impactor, as well as simply plotting the crater well volume V divided with cluster size N as a function of N. The macroscopic scaling laws correspond to the case where V=N is constant with N. Fig. 2 shows snapshots of an impact event where the atoms are coloured according to local atom density. The figures show that
0.8
500 eV/atom AuN on Au(111)
0.7 0.6
V/N
0.5 0.4 0.3 0.2
Linear macroscopic scaling
0.1 0.0
0
100000
200000
300000
N Fig. 3. Crater size as a function of impactor size for Au cluster impacts on Au with a constant energy of 500 eV/atom. The dashed line shows a downwards extrapolation from macroscopic crater size scaling laws with parameters specific to Au. The data is from [14].
both for impacts on Au and SiO2 the local material density below the impactor is roughly two times higher than the equilibrium density (up to four times higher densities have been observed in some of the simulations). This corresponds well to the density increases estimated e.g. for rock. Note that the case of SiO2 is especially important here, since rocks are typically silica-based compounds. Detailed analysis of the case of Au showed that the high-density region starts to form for impactor sizes above 500 atoms in Au but clear macroscopic behaviour is detected at 50,000 atoms and above [14]. This is very well in line with the result shown in Fig. 3, which shows that for impactor sizes above 50,000 the crater sizes behave as expected for macroscopic scaling. Comparison of cratering by spherical or cubic impactors showed that there was no statistically significant dependence on crater size with impactor shape. 4. Conclusions In conclusion, by carrying out cluster impact MD simulations on Au, Si and SiO2 , we have shown that the impact events start to behave like macroscopic impacts with respect to splash crown and corona formation for impactor sizes above roughly 100 atoms. Moreover, for impactor sizes above roughly 10,000 atoms, the crater formation mechanism becomes that known as the ‘strength’ regime for macroscopic impacts. Acknowledgements This work was performed within the Finnish Centre of Excellence in Computational Molecular Science (CMS), financed by The Academy of Finland and the University of Helsinki and also financed by Academy projects OPNA and CONADEP. Grants of computer time from the Centre for Scientific Computing in Espoo, Finland, are gratefully acknowledged. References [1] M.T. Robinson, I.M. Torrens, Phys. Rev. B 9 (1974) 5008. [2] K.L. Merkle, W. Jäger, Phil. Mag. A 44 (1980) 741. [3] T. Diaz de la Rubia, R.S. Averback, R. Benedek, W.E. King, Phys. Rev. Lett. 59 (1987) 1930 (See also erratum: Phys. Rev. Lett. 60 (1988) 76). [4] M. Ghaly, R.S. Averback, Phys. Rev. Lett. 72 (1994) 364. [5] R.C. Birtcher, S.E. Donnelly, Nucl. Instr. and Meth. B 148 (1999) 194. [6] H.M. Urbassek, K.T. Waldeer, Phys. Rev. Lett. 67 (1991) 105. [7] K. Nordlund, M. Ghaly, R.S. Averback, M. Caturla, T. Diaz de la Rubia, J. Tarus, Phys. Rev. B 57 (1998) 7556. [8] J.A. Brinkman, J. Appl. Phys. 25 (1954) 961. [9] R. Aderjan, H.M. Urbassek, Nucl. Instr. and Meth. B 164-165 (2000) 697. [10] M. Ghaly, K. Nordlund, R.S. Averback, Phil. Mag. A 79 (1999) 795. [11] M. Morgenstern, T. Michely, G. Comsa, Phil. Mag. A 79 (1999) 775. [12] J. Samela, K. Nordlund, Nucl. Instr. and Meth. B 263 (2007) 375. [13] J. Samela, K. Nordlund, New J. Phys. 10 (2007) 023013. [14] J. Samela, K. Nordlund, Phys. Rev. Lett. 101 (2008) 027601. and cover of issue 2. Also selected to Virtual J. Nanoscale Sci.& Technol. 18 (3) (2008). [15] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford University Press, Oxford, England, 1989. [16] K. Nordlund, 2006, (PARCAS computer code. The main principles of the molecular dynamics algorithms are presented in [7,10]. The adaptive time step and electronic stopping algorithms are the same as in [33]. [17] J. Tarus, K. Nordlund, A. Kuronen, J. Keinonen, Phys. Rev. B 58 (1998) 9907. [18] J. Samela, J. Kotakoski, K. Nordlund, J. Keinonen, Nucl. Instr. and Meth. B 239 (2005) 331. [19] J. Samela, K. Nordlund, Phys. Rev. B 76 (2007) 125434. [20] C.L. Kelchner, D.M. Halstead, L.S. Perkins, N.M. Wallace, A.E. DePristo, Surf. Sci. 310 (1994) 425. and references therein. [21] J. Samela, K. Nordlund, J. Keinonen, V.N. Popok, Nucl. Instr. and Meth. B 255 (2007) 253. [22] T. Watanabe, D. Yamasaki, K. Tatsumura, I. Ohdomari, Appl. Surf. Sci. 234 (2004) 207. [23] J. Samela, K. Nordlund, V.N. Popok, E.E.B. Campbell, Phys. Rev. B 77 (2008) 075309. This also has the description of the Samela–Watanabe potential. [24] F. Djurabekova, K. Nordlund, Phys. Rev. B 77 (2008) 115325; F. Djurabekova, K. Nordlund, Virtual J. Nanoscale Sci. & Technol. 17 (13) (2008).
K. Nordlund, J. Samela / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1420–1423 [25] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Matter, Pergamon, New York, 1985. [26] R.M. Schmidt, K.R. Housen, Intl. J. Impact Eng. 5 (1987) 543. [27] G. Neukum, B.A. Ivanov, Crater size distributions and impact probabilities on earth from lunar, terrestrial-planet, and asteroid cratering data, in: T. Gehrels (Ed.), Hazards due to Comets & Asteroids, Space Science, The University of Arizona Press, Tucson, Arizona, 1994, p. 359.
1423
[28] J.M. Walsh, G.L. Straddling, G.C. Idzorek, B.P. Shafer, W.X. Do, Int. J. Impact Eng. 14 (1993) 775. [29] S.G. Love, D.E. Brownlee, N.L. King, F. Hörz, Int. J. Impact Eng. 16 (1995) 405. [30] K.A. Holsapple, K.R. Housen, Icarus 187 (2007) 345. [31] A.L. Yarin, Annu. Rev. Fluid Mech. 38 (2006) 159. [32] V. Popok, S. Prasalovich, E. Campbell, Surf. Sci. 566–568 (2004) 1179. [33] K. Nordlund, Comput. Mater. Sci. 3 (1995) 448.
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Atomic flows, coronas and cratering in Au, Si and SiO2 Kai Nordlund *, Juha Samela Helsinki Institute of Physics and Department of Physics, University of Helsinki, P.O. Box 43, FI-00014, Finland
a r t i c l e
i n f o
Article history: Available online 3 February 2009 PACS: 79.20. m 61.80.Jh 83.10.Rs Keywords: Cratering Ion impacts Crater impacts Molecular dynamics simulation
a b s t r a c t The traditional picture of ion irradiation effects in materials was that of a series of binary collisions. Since the 1980’s it has, however, become clear that collective many-body effects such as heat spikes and flow of liquid matter can be important in dense metals. Now very recent atomistic simulations indicate that during MeV cluster ion bombardment, the irradiation effects start to resemble macroscopic phenomena such as the splashes and coronas observed when heavy objects fall on water. In this article, we review recent work showing that the craters formed during cluster impacts start to behave like macroscopic cratering beyond a certain impactor size. We also present new results which show that for cluster sizes of only around 100 atoms, not only dense metals, but also brittle materials like Si and SiO2 start to exhibit hydrodynamic-like behaviour of collective atom flow and corona formation. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction For a long time, the theoretical understanding of ion irradiation effects in materials was almost solely based on treating the irradiation process as a series of binary collisions [1]. While this kind of treatment certainly is adequate for a wide range of irradiation conditions, since the 1980’s it has started to become clear that also collective phenomena like formation of hot molten zones of matter and flow of atoms can be important and even dominate the behaviour [2–5]. This development of understanding naturally followed the computer capacity available. Until the 1980’s only computationally efficient binary collision approximation [1] methods were fast enough for practical use in simulation of collision cascades in the heat spike regime. However, when computers became fast enough in the 1990’s to treat many-body collisional effects of tens of thousands of atoms, molecular dynamics (MD) simulations could be used to directly simulate the heat spikes [3,6,4,7], the existence of which had in fact already been predicted in the 1950’s [8]. One intriguing heat spike phenomenon is the formation of craters on surfaces by the impacts of single atoms [2,4,5]. Ever since these were first observed, it was clear that they at least superficially resemble the craters formed on the surfaces of planets and moons by impacting meteoroids and asteroids. However, it has not been clear whether the mechanisms of atomic and macroscopic cratering are really the same, or whether the similarity is * Corresponding author. E-mail address: kai.nordlund@helsinki.fi (K. Nordlund). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.01.125
just coincidental. Some observations have indeed indicated that there must be a clear difference in the mechanisms. The scaling laws applied to macroscopic craters do not match those obtained on the atomic scale [9]. Moreover, for single ion impacts, large craters are observed on the surfaces of metals like Au but not brittle materials like Ge [10,11], even though almost all astronomical craters are of course formed on brittle rock-like materials. Now that computer capacity has advanced further from the 1990’s level, it is possible to simulate systems with tens of millions of atoms for the full duration of a collision cascade and its relaxation phase. This has enabled simulation of ion and cluster ion impacts with impactor energies exceeding well above 1 MeV. Such simulations have shown that in very large collisional systems, the behaviour starts in many ways to resemble purely macroscopic phenomena like flows, splash crown and corona formation and pressure-induced cratering [12–14]. In this article, we review our very recent work on metals that shows how the atomistic cratering transforms into the macroscopic one and present previously unpublished results on splash crowns in Si and SiO2 . 2. Method Ion and cluster ion impacts were simulated with classical molecular dynamics employing many-body interatomic potentials implemented in the PARCAS MD code [15,16]. The basic simulation methodology has been described in several previous works [7,17– 19], so here we only summarize the interaction models used, as this is relevant for understanding the comparison of materials. To simulate Au we used a corrected effective medium (CEM) potential
K. Nordlund, J. Samela / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1420–1423
which has been constructed to describe surfaces and small clusters [20]. It also describes well elasticity and melting of Au and has been found to predict sputtering yields which agree very well with experiments [18]. For Si we have tested a wide range of interatomic potentials and found that while none agrees with all experiments they have been compared against, most of them predict qualitatively similar crater formation and sputtering behaviour [21]. To simulate quartz and silica we employ the Stillinger–Weber-like potential by Watanabe and Samela [22,23]. This potential has the correct ground state of a-quartz, has been shown to describe well the structure of amorphous silica and can describe both pure Si and SiO2 in the same parametrisation [23,24]. For the Ar interactions we used the purely repulsive universal ZBL potential [25]. The projectiles were chosen to be Au (for impacts on Au) or Ar (for impacts on Si and SiO2 ) clusters in the size range 1–316,000 atoms. The shape was spherical or in some cases cubic to test whether the projectile shape affects the results. In all cases the projectiles were first independently relaxed at 300 K with an MD sim-
1421
ulation to ensure that they do not have extra internal energy that could effect the outcome. For the cubic projectiles, this lead to a smoothing of the edges due to surface atom migration.
3. Results and discussion Examination of how the atomic cratering transforms into the macroscopic one is made easier by the fact that the mechanisms of the latter kind are fairly well understood. Macroscopic cratering is usually divided in two regimes, the strength and gravity regimes [26,27]. In the former, the final crater size (for a given projectile and energy) is determined by the strength of the material, while in the latter also gravity plays a role. The gravity regime starts to emerge for impactors with sizes of tens of meters or more and is thus irrelevant in the current context. The strength regime is relevant to small meteoroids, but also projectiles from e.g. gas guns, bullets and micrometeorites [26,28,29].
Fig. 1. Snapshots from MD simulations of corona formation during cluster ion irradiation of Au and Si. The top two frames show bombardment of Au and bottom two of Si. For the Au cases the projectile as Au6800 at an energy of 500 eV/atom, for Si it was Ar147 at an energy of 400 eV/atom.
Fig. 2. Formation of a high-pressure region in (a) 500 eV/atom Au101000 impact on Au and (b) 100 eV/atom Ar100000 impact on SiO2 . The figures are snapshots where the colour (grey) scale shows the local atomic density around the atom divided by the normal equilibrium density. Blue (darker) spheres show normal or low densities and red (lighter) spheres show higher densities. The darkest red corresponds to an atom density of about three times the normal one. (For interpretation of the references in colour in this figure legend, the reader is referred to the web version of this article.)
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K. Nordlund, J. Samela / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1420–1423
In the strength regime, the basic reason to cratering is, based on experiments and hydrodynamic modelling, known to be the formation of a high-pressure region below the impactor [26,30,31]. When the high-pressure is released, a crown is formed, which subsequently breaks up leading to the emission of ejecta and formation of a crater rim. A similar process is known to occur for all kinds of materials, ranging from dense metals to sand, rock and liquids (in which case the crater is of course only transient). To find where the atomistic cratering mechanism transforms into the macroscopic one, we started with the insight that typical meteoroid impacts occur for velocities around 22 km/s, which when translated to kinetic energy means about 500 eV/atom for Au. This is of course, but purely coincidentally, a typical ion beam energy. We thus were able to use our existing ion beam MD codes and methods to systematically simulate bombardment of Au with increasingly large projectiles with a constant energy of 500 eV/ atom [14]. Since the kinetic energy (velocity) corresponds exactly to that of macroscopic impacts, the cratering mechanism presumably should for large enough projectile size transform into the macroscopic one. To obtain a point of comparison in brittle materials, for the current article, we also simulated Ar cluster impacts on Si. Recall that it is known that single atoms form no or only small craters or hillocks (height 0.5 nm or less) in Si or Ge [10,32,23], so appearance of macroscopic-like behaviour must occur for larger projectile sizes. Development of a splash crown and its subsequent breakup is illustrated in Fig. 1 for Au and Ar clusters. Clearly in both Au and Si a macroscopic-like hydrodynamic behaviour is present. To obtain a quantitative measure of whether the cratering mechanism really corresponds to the macroscopic ones, we have carried out several types of analyses of the cratering behaviour [19,12–14]. The most useful ones with respect to finding the transition to macroscopic behaviour have been analysis of the local density of each atom below the impactor, as well as simply plotting the crater well volume V divided with cluster size N as a function of N. The macroscopic scaling laws correspond to the case where V=N is constant with N. Fig. 2 shows snapshots of an impact event where the atoms are coloured according to local atom density. The figures show that
0.8
500 eV/atom AuN on Au(111)
0.7 0.6
V/N
0.5 0.4 0.3 0.2
Linear macroscopic scaling
0.1 0.0
0
100000
200000
300000
N Fig. 3. Crater size as a function of impactor size for Au cluster impacts on Au with a constant energy of 500 eV/atom. The dashed line shows a downwards extrapolation from macroscopic crater size scaling laws with parameters specific to Au. The data is from [14].
both for impacts on Au and SiO2 the local material density below the impactor is roughly two times higher than the equilibrium density (up to four times higher densities have been observed in some of the simulations). This corresponds well to the density increases estimated e.g. for rock. Note that the case of SiO2 is especially important here, since rocks are typically silica-based compounds. Detailed analysis of the case of Au showed that the high-density region starts to form for impactor sizes above 500 atoms in Au but clear macroscopic behaviour is detected at 50,000 atoms and above [14]. This is very well in line with the result shown in Fig. 3, which shows that for impactor sizes above 50,000 the crater sizes behave as expected for macroscopic scaling. Comparison of cratering by spherical or cubic impactors showed that there was no statistically significant dependence on crater size with impactor shape. 4. Conclusions In conclusion, by carrying out cluster impact MD simulations on Au, Si and SiO2 , we have shown that the impact events start to behave like macroscopic impacts with respect to splash crown and corona formation for impactor sizes above roughly 100 atoms. Moreover, for impactor sizes above roughly 10,000 atoms, the crater formation mechanism becomes that known as the ‘strength’ regime for macroscopic impacts. Acknowledgements This work was performed within the Finnish Centre of Excellence in Computational Molecular Science (CMS), financed by The Academy of Finland and the University of Helsinki and also financed by Academy projects OPNA and CONADEP. Grants of computer time from the Centre for Scientific Computing in Espoo, Finland, are gratefully acknowledged. References [1] M.T. Robinson, I.M. Torrens, Phys. Rev. B 9 (1974) 5008. [2] K.L. Merkle, W. Jäger, Phil. Mag. A 44 (1980) 741. [3] T. Diaz de la Rubia, R.S. Averback, R. Benedek, W.E. King, Phys. Rev. Lett. 59 (1987) 1930 (See also erratum: Phys. Rev. Lett. 60 (1988) 76). [4] M. Ghaly, R.S. Averback, Phys. Rev. Lett. 72 (1994) 364. [5] R.C. Birtcher, S.E. Donnelly, Nucl. Instr. and Meth. B 148 (1999) 194. [6] H.M. Urbassek, K.T. Waldeer, Phys. Rev. Lett. 67 (1991) 105. [7] K. Nordlund, M. Ghaly, R.S. Averback, M. Caturla, T. Diaz de la Rubia, J. Tarus, Phys. Rev. B 57 (1998) 7556. [8] J.A. Brinkman, J. Appl. Phys. 25 (1954) 961. [9] R. Aderjan, H.M. Urbassek, Nucl. Instr. and Meth. B 164-165 (2000) 697. [10] M. Ghaly, K. Nordlund, R.S. Averback, Phil. Mag. A 79 (1999) 795. [11] M. Morgenstern, T. Michely, G. Comsa, Phil. Mag. A 79 (1999) 775. [12] J. Samela, K. Nordlund, Nucl. Instr. and Meth. B 263 (2007) 375. [13] J. Samela, K. Nordlund, New J. Phys. 10 (2007) 023013. [14] J. Samela, K. Nordlund, Phys. Rev. Lett. 101 (2008) 027601. and cover of issue 2. Also selected to Virtual J. Nanoscale Sci.& Technol. 18 (3) (2008). [15] M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford University Press, Oxford, England, 1989. [16] K. Nordlund, 2006, (PARCAS computer code. The main principles of the molecular dynamics algorithms are presented in [7,10]. The adaptive time step and electronic stopping algorithms are the same as in [33]. [17] J. Tarus, K. Nordlund, A. Kuronen, J. Keinonen, Phys. Rev. B 58 (1998) 9907. [18] J. Samela, J. Kotakoski, K. Nordlund, J. Keinonen, Nucl. Instr. and Meth. B 239 (2005) 331. [19] J. Samela, K. Nordlund, Phys. Rev. B 76 (2007) 125434. [20] C.L. Kelchner, D.M. Halstead, L.S. Perkins, N.M. Wallace, A.E. DePristo, Surf. Sci. 310 (1994) 425. and references therein. [21] J. Samela, K. Nordlund, J. Keinonen, V.N. Popok, Nucl. Instr. and Meth. B 255 (2007) 253. [22] T. Watanabe, D. Yamasaki, K. Tatsumura, I. Ohdomari, Appl. Surf. Sci. 234 (2004) 207. [23] J. Samela, K. Nordlund, V.N. Popok, E.E.B. Campbell, Phys. Rev. B 77 (2008) 075309. This also has the description of the Samela–Watanabe potential. [24] F. Djurabekova, K. Nordlund, Phys. Rev. B 77 (2008) 115325; F. Djurabekova, K. Nordlund, Virtual J. Nanoscale Sci. & Technol. 17 (13) (2008).
K. Nordlund, J. Samela / Nuclear Instruments and Methods in Physics Research B 267 (2009) 1420–1423 [25] J.F. Ziegler, J.P. Biersack, U. Littmark, The Stopping and Range of Ions in Matter, Pergamon, New York, 1985. [26] R.M. Schmidt, K.R. Housen, Intl. J. Impact Eng. 5 (1987) 543. [27] G. Neukum, B.A. Ivanov, Crater size distributions and impact probabilities on earth from lunar, terrestrial-planet, and asteroid cratering data, in: T. Gehrels (Ed.), Hazards due to Comets & Asteroids, Space Science, The University of Arizona Press, Tucson, Arizona, 1994, p. 359.
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[28] J.M. Walsh, G.L. Straddling, G.C. Idzorek, B.P. Shafer, W.X. Do, Int. J. Impact Eng. 14 (1993) 775. [29] S.G. Love, D.E. Brownlee, N.L. King, F. Hörz, Int. J. Impact Eng. 16 (1995) 405. [30] K.A. Holsapple, K.R. Housen, Icarus 187 (2007) 345. [31] A.L. Yarin, Annu. Rev. Fluid Mech. 38 (2006) 159. [32] V. Popok, S. Prasalovich, E. Campbell, Surf. Sci. 566–568 (2004) 1179. [33] K. Nordlund, Comput. Mater. Sci. 3 (1995) 448.