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Historical Review of Computer Simulation of Radiation Effects in Materials

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Historical Review of Computer Simulation of Radiation Effects in Materials Journal of Nuclear Materials 520 (2019) 273e295 Contents lists available at ScienceDirect Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat Historical review of computer simulation of radiation effects in materials K. Nordlund Department of Physics, P. O. Box 43, FIN-00014, University of Helsinki, Finland article info abstract Article history: In this Article, I review the development of computer simulation techniques for studying radiation effects Received 28 October 2018 in materials from 1946 until 2018. These developments were often closely intertwined with associated Received in revised form experimental developments, which are also briefly discussed in conjunction with the simulations. The 31 March 2019 focus is on methods that either deal directly with the primary radiation damage generation event, or Accepted 22 April 2019 with such defects or phase changes that typically occur due to radiation. The methods discussed at some Available online 6 May 2019 length are, in order of historical appearance: Reaction rate theory or rate equations (RE), Monte Carlo neutronics calculations (MCN), Metropolis Monte Carlo (MMC), Molecular Dynamics (MD), Binary Collision Approximation (BCA), Kinetic Monte Carlo (KMC), Discrete Dislocation Dynamics (DDD), Time- Dependent Density Functional Theory (TDDFT), and Finite Element Modelling (FEM). For each method, I present the origins of the methods, some key developments after this, as well as give some opinions on possible future development paths. © 2019 The Author. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Contents 1. Introduction . ................................................ 273 2. Overview of physics and methods . ........................................... 274 3. Reaction rate theory or rate equations (RE) . ................................... 276 4. Monte Carlo neutronics calculations (MCN) . .. ................................... 278 5. Metropolis Monte Carlo (MMC) . ........................................... 278 6. Molecular dynamics (MD) . ................................................ 279 6.1. MD in recoil interaction approximation (RIA) . .......................281 7. Binary collision approximation (BCA) . ........................................... 282 7.1. Kinetic Monte Carlo (KMC) . .......................282 8. Discrete Dislocation Dynamics (DDD) . ........................................... 284 9. Density functional theory (DFT) . ........................................... 284 10. Time-Dependent Density Functional Theory (TDDFT) . ................................... 285 11. Finite element methods (FEM) . ............................................... 286 12. Comparative discussion . ................................................ 286 13. Conclusions . ................................................ 287 Acknowledgements . .......................288 References.................................................................................................. .......................288 1. Introduction In this Article, I review the development of computer simulation techniques for studying radiation effects in materials. The topic of E-mail address: kai.nordlund@helsinki.fi. https://doi.org/10.1016/j.jnucmat.2019.04.028 0022-3115/© 2019 The Author. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 274 K. Nordlund / Journal of Nuclear Materials 520 (2019) 273e295 “radiation” is in this article understood as ionizing radiation or either molecular dynamics or density functional theory. Out of atomic collision processes, i.e. effects of particles with energies high these, about 500 were also related to radiation effects (purely enough to cause ionization and/or permanent defect production in coincidentally, in 2017 the numbers are about the same for both solid materials (i.e. effects of visible light radiation are excluded). In methods). In other words, for these methods, the radiation effects general, the study of radiation effects of course predates the exis- studies are only about 3.5% of the total. tence of electronic computers and even mechanical computers. The I note that the topic of the origin of these simulation methods is first report of scientific study of radiation effects can be considered interesting not only for radiation effects specialists, but also for the to be from Grove in 1852 [1], and the history of modern physics was development of computational physics and numerical mathematics closely related to the development of radiation effects science in general. Examples of this are given for some of the methods [2e7]. below. Study of radiation effects also had a profound influence on the In the remainder of the article, for the methods listed above, I much broader field of computational science, as the very first give a very brief description of how the method works is given; for computer simulations ever performed in any field of science, were each of the methods, there are textbook-length treatments avail- on radiation effects. Also, the developments on radiation effect able, so giving a comprehensive description is not possible in a simulations were often closely intertwined with experimental de- limited-length review article. For each method, my best knowledge velopments, and relevant experiments are also briefly mentioned of their history is given, followed by some highlights of their in conjunction with the simulations. development over the years. The total number of publications un- The focus of this article is on methods that either deal directly derlying the data on the methods and radiation in Fig. 3 is 19600, with the primary radiation damage generation event, or with such and I do not attempt a comprehensive review of this vast body of defects or phase changes that typically occur due to radiation, but work. less often in near-equilibrium materials processing. General in- At the end of the article, there is also a general discussion about troductions to computer simulation methods in physics are given in how the use of the methods has developed over the years, and several books, e.g. Refs. [8e10], however, in this article we focus on some general outlook for the future. radiation-relevant methods. For this topic, also several books have been previously written (e.g. Refs. [8,11,12], however, these did not 2. Overview of physics and methods deal with all of the methods discussed in this review article. Each method is presented in a separate section, organized as In an attempt to give a reader a view how the different methods follows. At first I give a very brief summary of the basic idea of the relate to each other, I first give a very brief overview of radiation method is given, with references to review articles or books where effects, linking the physics stages to different simulation methods. much more detail is given. Then I present the origins of the method Other articles in this anniversary volume discuss the physics of the are given, with an attempt to provide the original scientific refer- different stages in greater detail. Radiation effects physics is also ence to each method. After this, instead of an attempt at a discussed at much wider extent e.g. in Refs. [12,15e17]. This section comprehensive review, I present a few key milestones in the is organized as the frames in Fig. 1, which are referred to in the method development, up to the present date. I also give a personal, following with uppercase letters A-F. The methods relevant to each and necessarily partly subjective, opinion on the outlook for the use stage are mentioned briefly with the abbreviations here, while the of the methods in the future. For those methods which are typically detailed method descriptions are given in the following Sections run with a few well-established computer codes, I also mention 4e12. these. The methods discussed at length are, in order of historical A) In the bulk, a radiation damage event is initiated by a passing appearance: Rate theory or rate equations (RE, section 3), Monte high-energy particle. This may be a high-energy (100's of Carlo neutronics calculations (MCN, section 4), Metropolis Monte keV's or MeV's) ion, neutron or electron. The passing particle Carlo (MMC, section 5), Molecular Dynamics (MD, section 6), Binary occasionally collides strongly with an atom in the material. If Collision Approximation (BCA, section 7), Kinetic Monte Carlo the energy transfer to this primary knock-on atom (PKA) ex- (KMC, section 7), Discrete Dislocation Dynamics (DDD, section 9), ceeds the threshold displacement energy [18,19], it starts Density Functional Theory (DFT, section 10), Time-Dependent moving ballistically between other lattice atoms. It will in Density Functional Theory (TDDFT, section 11), and Finite Element turn collide with other atoms (secondary knock-on atoms), Modelling (FEM, section 12). and so on. The sequence of collisions is called a collision While preparing the article, I also considered the crystal plas- cascade. This initial stage is not a thermodynamic system, ticity (CP) [13] and phase field modelling (PFM) [14] methods. The since the time scale of the high-energy collisions 10 fs) is number of works on these methods and irradiation using the same much shorter than the lattice vibration frequency of solids search criteria as for the other methods was, however, relatively 300 fs [20]). small, so that I considered
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