225:
169:
337:
324:. Unfortunately the rate of electron-phonon coupling from the hot and disordered ionic system is not well known, as it can not be treated equally to the fairly well known process of transfer of heat from hot electrons to an intact crystal structure. Finally, the relaxation phase of the cascade, when the defects formed possibly recombine and migrate, can last from a few ps to infinite times, depending on the material, its
150:
2225:
197:(MD) simulations. In MD simulations they can be included either as a frictional force or in a more advanced manner by also following the heating of the electronic systems and coupling the electronic and atomic degrees of freedom. However, uncertainties remain on what is the appropriate low-energy limit of electronic stopping power or electron-phonon coupling is.
421:, both in the linear spike and heat spike regimes. Heat spikes near surfaces also frequently lead to crater formation. This cratering is caused by liquid flow of atoms, but if the projectile size above roughly 100,000 atoms, the crater production mechanism switches to the same mechanism as that of macroscopic craters produced by bullets or asteroids.
257:(the two terms are usually considered to be equivalent). The heat spike cools down to the ambient temperature in 1–100 ps, so the "temperature" here does not correspond to thermodynamic equilibrium temperature. However, it has been shown that after about 3 lattice vibrations, the kinetic energy distribution of the atoms in a heat spike has the
320:, typically lasts 0.1–0.5 ps. If a heat spike is formed, it can live for some 1–100 ps until the spike temperature has cooled down essentially to the ambient temperature. The cooling down of the cascade occurs via lattice heat conductivity and by electronic heat conductivity after the hot ionic subsystem has heated up the electronic one via
261:, making the use of the concept of temperature somewhat justified. Moreover, experiments have shown that a heat spike can induce a phase transition which is known to require a very high temperature, showing that the concept of a (non-equilibrium) temperature is indeed useful in describing collision cascades.
408:
A curious feature of collision cascades is that the final amount of damage produced may be much less than the number of atoms initially affected by the heat spikes. Especially in pure metals, the final damage production after the heat spike phase can be orders of magnitude smaller than the number of
228:
As above, but in the middle the region of collisions has become so dense that multiple collisions occur simultaneously, which is called a heat spike. In this region the ions move in complex paths, and it is not possible to distinguish the numerical order of recoils - hence the atoms are colored with
216:
When the ion is heavy and energetic enough, and the material is dense, the collisions between the ions may occur so near to each other that they can not be considered independent of each other. In this case the process becomes a complicated process of many-body interactions between hundreds and tens
276:
For instance, for copper irradiation of copper, recoil energies of around 5–20 keV are almost guaranteed to produce heat spikes. At lower energies, the cascade energy is too low to produce a liquid-like zone. At much higher energies, the Cu ions would most likely lead initially to a linear cascade,
348:
simulation of a collision cascade. The image shows a cross section of two atomic layers in the middle of a threedimensional simulation cell. Each sphere illustrates the position of an atom, and the colors show the kinetic energy of each atom as indicated by the scale on the right. At the end, both
172:
Schematic illustration of a linear collision cascade. The thick line illustrates the position of the surface, and the thinner lines the ballistic movement paths of the atoms from beginning until they stop in the material. The purple circle is the incoming ion. Red, blue, green and yellow circles
204:(PKA), secondary knock-on atoms (SKA), tertiary knock-on atoms (TKA), etc. Since it is extremely unlikely that all energy would be transferred to a knock-on atom, each generation of recoil atoms has on average less energy than the previous, and eventually the knock-on atom energies go below the
409:
atoms displaced in the spike. On the other hand, in semiconductors and other covalently bonded materials the damage production is usually similar to the number of displaced atoms. Ionic materials can behave like either metals or semiconductors with respect to the fraction of damage recombined.
272:
is low. But once the Cu ion would slow down enough, the nuclear stopping power would increase and a heat spike would be produced. Moreover, many of the primary and secondary recoils of the incoming ions would likely have energies in the keV range and thus produce a heat spike.
27:
42:
Au self-recoil. This is a typical case of a collision cascade in the heat spike regime. Each small sphere illustrates the position of an atom, in a 2-atom-layer-thick cross section of a three-dimensional simulation cell. The colors show (on a logarithmic scale) the
397:
The defects production can be harmful, such as in nuclear fission and fusion reactors where the neutrons slowly degrade the mechanical properties of the materials, or a useful and desired materials modification effect, e.g., when ions are introduced into
315:
To understand the nature of collision cascade, it is very important to know the associated time scale. The ballistic phase of the cascade, when the initial ion/recoil and its primary and lower-order recoils have energies well above the
299:, can also be considered to produce thermal spikes in the sense that they lead to strong lattice heating and a transient disordered atom zone. However, at least the initial stage of the damage might be better understood in terms of a
161:), the collisions between the initial recoil and sample atoms occur rarely, and can be understood well as a sequence of independent binary collisions between atoms. This kind of a cascade can be theoretically well treated using the
233:
Typically, a heat spike is characterized by the formation of a transient underdense region in the center of the cascade, and an overdense region around it. After the cascade, the overdense region becomes
424:
The fact that many atoms are displaced by a cascade means that ions can be used to deliberately mix materials, even for materials that are normally thermodynamically immiscible. This effect is known as
200:
In linear cascades the set of recoils produced in the sample can be described as a sequence of recoil generations depending on how many collision steps have passed since the original collision:
249:
T), one finds that the kinetic energy in units of temperature is initially of the order of 10,000 K. Because of this, the region can be considered to be very hot, and is therefore called a
321:
2151:
1219:
185:. Note, however, that SRIM does not treat effects such as damage due to electronic energy deposition or damage produced by excited electrons. The nuclear and electronic
19:
For the scenario of collisions between objects in low earth orbit producing a chain reactions of debris colliding with additional objects producing more debris, see
1609:
A. Struchbery; E. Bezakova (1999). "Thermal-Spike
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Pugacheva, T; Gjurabekova, F; Khvaliev, S (1998). "Effects of cascade mixing, sputtering and diffusion by high dose light ion irradiation of boron nitride".
2149:
T. Pugacheva; F. Gjurabekova; S. Khvaliev (1998). "Effects of cascade mixing, sputtering and diffusion by high dose light ion irradiation of boron nitride".
366:
Since the kinetic energies in a cascade can be very high, it can drive the material locally far outside thermodynamic equilibrium. Typically this results in
452:
165:(BCA) simulation approach. For instance, H and He ions with energies below 10 keV can be expected to lead to purely linear cascades in all materials.
157:
When the initial recoil/ion mass is low, and the material where the cascade occurs has a low density (i.e. the recoil-material combination has a low
432:
The non-equilibrium nature of irradiation can also be used to drive materials out of thermodynamic equilibrium, and thus form new kinds of alloys.
173:
illustrate primary, secondary, tertiary and quaternary recoils, respectively. In between the ballistic collisions the ions move in a straight path.
485:
R. S. Averback and T. Diaz de la Rubia (1998). "Displacement damage in irradiated metals and semiconductors". In H. Ehrenfest; F. Spaepen (eds.).
189:
used are averaging fits to experiments, and are thus not perfectly accurate either. The electronic stopping power can be readily included in
137:
The nature of collision cascades can vary strongly depending on the energy and mass of the recoil/incoming ion and density of the material (
245:
If the kinetic energy of the atoms in the region of dense collisions is recalculated into temperature (using the basic equation E = 3/2·N·k
1728:
M. O. Ruault; J. Chaumont; J. M. Penisson; A. Bourret (1984). "High resolution and in situ investigation of defects in Bi-irradiated Si".
281:
signifies the energy above which a recoil in a material is likely to produce several isolated heat spikes rather than a single dense one.
340:
Image sequence of the time development of a collision cascade in the heat spike regime produced by a 30 keV Xe ion impacting on Au under
1766:
303:
mechanism. Regardless of what the heating mechanism is, it is well established that swift heavy ions in insulators typically produce
938:
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Robinson, M. T. (1974). "Computer
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can be used to simulate linear collision cascades in disordered materials for all ion in all materials up to ion energies of 1
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1916:
1816:
V. D. S. Dhaka; et al. (2006). "Ultrafast dynamics of Ni+-irradiated and annealed GaInAs/InP multiple quantum wells".
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but the recoils could lead to heat spikes, as would the initial ion once it has slowed down enough. The concept
190:
162:
284:
Computer simulation-based animations of collision cascades in the heat spike regime are available on YouTube.
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2195:
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870:
824:
787:
721:
670:
627:
555:
115:
2051:
M. Ghaly; R. Averback (1994). "Effect of viscous flow on ion damage near solid surfaces".
1154:"A transient liquid-like phase in the displacement cascades of zircon, hafnon and thorite"
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1524:
1505:
P. Kluth; et al. (2008). "Fine
Structure in Swift Heavy Ion Tracks in Amorphous SiO
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of thousands of atoms, which can not be treated with the BCA, but can be modelled using
2131:
1996:
1941:
1896:
1843:
1591:
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1280:
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218:
194:
31:
2207:
2172:
1937:
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131:
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800:
775:
698:
647:
405:
structures to speed up the operation of a laser. or to strengthen carbon nanotubes.
2203:
2168:
2119:
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1986:
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1002:
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72:
44:
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Series of collisions between nearby atoms, initiated by a single energetic atom
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1669:
1343:
898:"The effect of electronic energy loss on the dynamics of thermal spikes in Cu"
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776:"Electron promotion and electronic friction in atomic collision cascades"
379:
354:
168:
622:
1991:
1587:
1479:"Swift heavy ion-induced modification and track formation in materials"
1050:
418:
304:
1414:
E. Bringa; R. Johnson (2002). "Coulomb
Explosion and Thermal Spikes".
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208:
for damage production, at which point no more damage can be produced.
2148:
1884:
1795:
1714:
1541:
383:
328:
migration and recombination properties, and the ambient temperature.
153:
Schematic illustration of independent binary collisions between atoms
76:
1364:
295:, i.e. MeV and GeV heavy ions which produce damage by a very strong
336:
123:
106:
or more), the collisions can permanently displace atoms from their
71:) is a set of nearby adjacent energetic (much higher than ordinary
47:
of the atoms, with white and red being high kinetic energy from 10
1182:
149:
119:
2224:
265:
127:
88:
417:
Collision cascades in the vicinity of a surface often lead to
2188:
Nuclear Instruments and Methods in Physics Research Section B
2152:
Nuclear Instruments and Methods in Physics Research Section B
1220:
Nuclear Instruments and Methods in Physics Research Section B
84:
26:
2185:
1152:
A. Meldrum; S.J. Zinkle; L. A. Boatner; R. C. Ewing (1998).
80:
35:
307:
forming long cylindrical damage zones of reduced density.
238:, and the underdense region typically becomes a region of
182:
114:. The initial energetic atom can be, e.g., an ion from a
95:
48:
39:
1608:
1767:"Ion beams in silicon processing and characterization"
1316:
A. Meftah; et al. (1994). "Track formation in SiO
534:
1216:
1087:
118:, an atomic recoil produced by a passing high-energy
2095:
2013:
98:
energies in a collision cascade are higher than the
2050:
1413:
1958:
1690:
1365:C. Trautmann; S. KlaumĂĽnzer; H. Trinkaus (2000).
344:conditions. The image is produced by a classical
287:
2237:
211:
1815:
34:computer simulation of a collision cascade in
1913:
130:, or be produced when a radioactive nucleus
1563:
1476:
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1990:
1764:
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1320:quartz and the thermal-spike mechanism".
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370:production. The defects can be, e.g.,
83:induced by an energetic particle in a
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2007:
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279:subcascade breakdown threshold energy
1917:Journal of Physics: Condensed Matter
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361:
134:and gives the atom a recoil energy.
863:Nucl. Instrum. Methods Phys. Res. B
814:
714:Nucl. Instrum. Methods Phys. Res. B
13:
144:
14:
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2217:
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177:The most commonly used BCA code
2179:
1854:
1809:
1765:E. Chason; et al. (1997).
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974:
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889:
808:
767:
2120:10.1103/PhysRevLett.101.027601
1533:10.1103/PhysRevLett.101.175503
740:
705:
654:
601:
574:
539:
528:
288:Swift heavy ion thermal spikes
259:Maxwell–Boltzmann distribution
191:binary collision approximation
163:binary collision approximation
51:downwards, and blue being low.
1:
2208:10.1016/S0168-583X(98)00139-6
2173:10.1016/S0168-583X(98)00139-6
1448:10.1103/PhysRevLett.88.165501
1298:"displacement cascade" Search
1237:10.1016/S0168-583X(99)01111-8
1038:10.1016/j.jnucmat.2014.06.007
960:10.1088/0953-8984/19/1/016207
905:Journal of Materials Research
734:10.1016/s0168-583x(01)00418-9
463:
318:threshold displacement energy
310:
206:threshold displacement energy
100:threshold displacement energy
595:10.1016/0927-0256(94)00085-q
212:Heat spikes (thermal spikes)
7:
1983:10.1103/PhysRevLett.50.1478
1938:10.1088/0953-8984/16/49/R03
1840:10.1088/0022-3727/39/13/004
1633:10.1103/PhysRevLett.82.3637
1393:10.1103/PhysRevLett.85.3648
1131:10.1103/PhysRevLett.59.1930
435:
382:loops, stacking faults, or
10:
2267:
2075:10.1103/PhysRevLett.72.364
1775:Journal of Applied Physics
1003:10.1103/PhysRevB.94.014305
883:10.1016/j.nimb.2009.03.080
512:Cambridge University Press
448:Radiation material science
331:
229:a mixture of red and blue.
18:
2038:10.1080/01418618808204681
1752:10.1080/01418618408237526
1670:10.1103/PhysRevB.47.14011
1344:10.1103/PhysRevB.49.12457
940:J. Phys.: Condens. Matter
801:10.1088/1367-2630/9/2/038
761:10.1080/10420159708211586
683:10.1103/PhysRevB.54.16683
102:of the material (tens of
2246:Condensed matter physics
2017:Philosophical Magazine A
1731:Philosophical Magazine A
1277:10.1103/PhysRevB.57.7556
1075:10.1103/PhysRev.120.1229
837:10.1103/PhysRevB.62.2825
640:10.1103/PhysRevE.57.7278
378:, ordered or disordered
322:electron–phonon coupling
57:condensed-matter physics
2099:Physical Review Letters
2054:Physical Review Letters
1962:Physical Review Letters
1694:Applied Physics Letters
1612:Physical Review Letters
1512:Physical Review Letters
1417:Physical Review Letters
1372:Physical Review Letters
1110:Physical Review Letters
568:10.1103/physrevb.9.5008
94:If the maximum atom or
896:Pronnecke, S. (1991).
774:Duvenbeck, A. (2007).
504:R. Smith, ed. (1997).
358:
230:
202:primary knock-on atoms
174:
154:
52:
925:10.1557/jmr.1991.0483
749:Rad. Eff. Def. In Sol
339:
227:
171:
152:
29:
2232:at Wikimedia Commons
1819:Journal of Physics D
1477:D. Kanjijal (2001).
1223:. 164–165: 697–704.
236:interstitial defects
116:particle accelerator
65:displacement cascade
2200:1998NIMPB.141...99P
2165:1998NIMPB.141...99P
2112:2008PhRvL.101b7601S
2067:1994PhRvL..72..364G
2030:1988PMagA..57..479J
1975:1983PhRvL..50.1478W
1930:2004JPCM...16R1491T
1924:(49): R1491–R1515.
1877:2004NatMa...3..153K
1832:2006JPhD...39.2659D
1788:1997JAP....81.6513C
1744:1984PMagA..50..667R
1707:1999ApPhL..74.2720N
1662:1993PhRvB..4714011K
1656:(21): 14011–14019.
1625:1999PhRvL..82.3637S
1580:1985ApPhA..37...37A
1525:2008PhRvL.101q5503K
1440:2002PhRvL..88p5501B
1385:2000PhRvL..85.3648T
1336:1994PhRvB..4912457M
1330:(18): 12457–12463.
1269:1998PhRvB..57.7556N
1229:2000NIMPB.164..697A
1175:1998Natur.395...56M
1123:1987PhRvL..59.1930D
1090:Solid State Physics
1067:1960PhRv..120.1229G
1030:2014JNuM..455..207S
995:2016PhRvB..94a4305L
952:2007JPCM...19a6207D
917:1991JMatR...6..483P
875:2009NIMPB.267.1830B
829:2000PhRvB..62.2825H
792:2007NJPh....9...38D
726:2001NIMPB.180..203H
675:1996PhRvB..5416683C
669:(23): 16683–16695.
632:1998PhRvE..57.7278B
560:1974PhRvB...9.5008R
493:. pp. 281–402.
487:Solid State Physics
297:electronic stopping
1588:10.1007/BF00617867
583:Comput. Mater. Sci
453:COSIRES conference
413:Other consequences
359:
346:molecular dynamics
231:
219:molecular dynamics
195:molecular dynamics
175:
155:
110:sites and produce
69:displacement spike
53:
32:molecular dynamics
2251:Radiation effects
2230:Collision cascade
2228:Media related to
1826:(13): 2659–2663.
1782:(10): 6513–6561.
1649:Physical Review B
1567:Applied Physics A
1323:Physical Review B
1263:(13): 7556–7570.
1256:Physical Review B
1117:(17): 1930–1933.
362:Damage production
301:Coulomb explosion
63:(also known as a
61:collision cascade
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489:. Vol. 51.
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388:ion implantation
293:Swift heavy ions
73:thermal energies
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21:Kessler syndrome
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145:Linear cascades
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1800:the original
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1302:YouTube.com
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823:(4): 2825.
780:New J. Phys
616:(6): 7278.
380:dislocation
355:dislocation
2240:Categories
2024:(3): 479.
1738:(5): 667.
911:(3): 483.
589:(4): 448.
554:(12): 12.
464:References
419:sputtering
390:doping of
342:channeling
311:Time scale
305:ion tracks
251:heat spike
77:collisions
2001:120756958
1946:123658664
1542:10440/862
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384:amorphous
374:such as
240:vacancies
221:methods.
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124:electron
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1971:Bibcode
1926:Bibcode
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991:Bibcode
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871:Bibcode
825:Bibcode
788:Bibcode
722:Bibcode
691:9985796
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628:Bibcode
556:Bibcode
332:Effects
120:neutron
112:defects
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326:defect
132:decays
128:photon
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1997:S2CID
1942:S2CID
1897:S2CID
1844:S2CID
1803:(PDF)
1770:(PDF)
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1197:S2CID
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841:S2CID
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85:solid
81:atoms
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516:ISBN
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