Hostname: page-component-76fb5796d-vvkck Total loading time: 0 Render date: 2024-04-25T14:29:42.746Z Has data issue: false hasContentIssue false
  • English
  • Français

Continuum approaches for modeling radiation-induced self-organization in materials: From the rate theory to the phase field approach

Published online by Cambridge University Press:  02 February 2018

David Simeone ,
Joel Ribis  and
Laurence Luneville
David Simeone*
Affiliation:
CEA/DEN/DMN/SRMA/LA2M-LRC CARMEN, CEA, Université Paris-Saclay, Gif-sur-Yvette F-91191, France; and CNRS/CentraleSupelec/UMR 8580, 3 rue Joliot-Curie, 9119 Gif sur Yvette, France
Joel Ribis
Affiliation:
CEA/DEN/DMN/SRMA/LA2M-LRC CARMEN, CEA, Université Paris-Saclay, Gif-sur-Yvette F-91191, France; and CNRS/CentraleSupelec/UMR 8580, 3 rue Joliot-Curie, 9119 Gif sur Yvette, France
Laurence Luneville
Affiliation:
CEA/DEN/DMN/SRMA/LA2M-LRC CARMEN, CEA, Université Paris-Saclay, Gif-sur-Yvette F-91191, France; and CNRS/CentraleSupelec/UMR 8580, 3 rue Joliot-Curie, 9119 Gif sur Yvette, France
*
a)Address all correspondence to this author. e-mail: david.simeone@cea.fr
Get access

Abstract

Microstructural patterns resulting from self-organization are responsible for phase transitions and property changes in many materials maintained far from the thermodynamic equilibrium. Understanding the origin and the selection of possible spatiotemporal patterns for dissipative systems, i.e., systems for which the energy is not conserved, is a major theme of research opening doors to many technological applications ranging from plasmonics to metamaterials. Almost forty years after Turing’s seminal paper on patterning, progress on modeling instabilities leading to pattern formation has been achieved. The first part of this work demonstrates that main field approaches succeeded in capturing the underlying physics responsible for the formation of radiation-induced spatiotemporal patterns experimentally observed. The second part of the text highlights the interest of the phase field method, a self-consistent mean field approach, to discuss the evolution of these patterns in a universal picture neglecting specific aspects of radiation-induced dynamics.

Keywords

nanostructureradiation effectssimulation
Type
Reviews
Information
Journal of Materials Research , Volume 33 , Issue 4 , 28 February 2018 , pp. 440 - 454
Check for updates
Copyright
Copyright © Materials Research Society 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This section of Journal of Materials Research is reserved for papers that are reviews of literature in a given area.

References

REFERENCES

Millet, P. and Tonks, M.: Application of phase-field modeling to irradiation effects in materials. Curr. Opin. Solid State Mater. Sci. 15, 125 (2011).Google Scholar
Li, Y., Hu, S., and Stan, M.: Application of the phase field method in predicting microstructure and property evolution of irradiated nuclear materials. npj Comput. Mater. 3, 16 (2017).CrossRefGoogle Scholar
Hu, S. and Lu, W.: Dynamics of the self assembly of nanovoids and nanobubbles in solids. Acta Mater. 53, 1799 (2005).Google Scholar
Hu, S. and Henager, C.: Phase-field modeling of void lattice formation under irradiation. J. Nucl. Mater. 394, 155 (2009).Google Scholar
Hu, S., Burkes, E., Lavender, C., Senor, J., Setyawan, W., and Xu, Z.: Formation mechanism of gaz bubble superlattice in UMo metal fuels: Phase-field modeling investigation. J. Nucl. Mater. 479, 202 (2016).Google Scholar
Khatchaturyan, A.G.: Theory of Structural Transformation in Solids (Wiley Interscience, New York, New York, 1983).Google Scholar
Tolédano, P. and Dmitriev, V.: Reconstructive Phase Transitions: In Crystals and Quasicrystals (World Scientific, Singapore, 1996).Google Scholar
Elder, K., Katakowski, M., Haataja, M., and Grant, M.: Modelling elasticity in crystal growth. Phys. Rev. Lett. 88, 245701 (2002).Google Scholar
Ghoniem, N. and Walgraef, D.: Instabilities and Self Organization in Materials, Vol. I (Oxford Science Publications, Oxford, United Kingdom, 2008).Google Scholar
Nicolis, G. and Prigogine, I.: Self Organization in Nonequilibrium Systems: From Dissipative Structure to Order through Fluctuations (Wiley, New York, 1977).Google Scholar
Van Kampen, G.: Processes in Physics and Chemistry (Amsterdam, New York, 1980).Google Scholar
Simeone, D., Costantini, J., Luneville, L., Desgranges, L., Trocellier, P., and Garcia, P.: Focus issue: Characterization and modeling of radiation damage on materials: State of the art, challenges, and protocols. J. Mater. Res. 30, 1495 (2015).CrossRefGoogle Scholar
Krishan, K.: Self-organization and void ordering during irradiation. Nature 287, 420 (1980).CrossRefGoogle Scholar
Jager, W., Erhart, D., Schilling, W., Dworschak, F., Gadalla, A., and Tsukuda, N.: Peroidic 001 walls of defects in proton-irradiated Cu and Ni. Mater. Sci. Forum 15–18, 881–888 (1988).Google Scholar
Jager, W. and Trinkaus, H.: Defect ordering in metals under irradiation. J. Nucl. Mater. 205, 3949 (1993).Google Scholar
Karlin, S. and Taylor, H.M.: A First Course in Stochastic Processes (Academic Press, New York, 1975).Google Scholar
Gillespie, D.: Stochastic simulation of chemical kinetics. Annu. Rev. Phys. Chem. 58, 35 (2007).CrossRefGoogle ScholarPubMed
Binder, K. and Stauffer, D.: Statistical theory of nucleation, condensation and coagulation. J. Adv. Phys. 25, 343 (1976).Google Scholar
Waite, T.: General theory of bimolecular reaction rates in solids and liquids. J. Chem. Phys. 28, 103 (1958).Google Scholar
Abromeit, C. and Wollenberg, H.: Elements of the radiation-induced structural self-organisation in materials. J. Mater. Res. 3, 640 (1988).Google Scholar
Nichols, F.: On the estimation of sink-absorption terms in reaction-rate-theory analysis of radiation damage. J. Nucl. Mater. 75, 32 (1978).CrossRefGoogle Scholar
Sigmund, P. and Gras-Marti, A.: Theoretical aspects of atomic mixing by ion beams. Nucl. Instrum. Methods Phys. Res., Sect. B 182, 211–219 (1981).Google Scholar
Simeone, D. and Luneville, L.: Concentration profile distortion under ion beam mixing: An example of levy flight. Phys. Rev. E 81, 021115 (2010).Google Scholar
Kiritani, M.: Radiation effect in breeder reactor structural materials. In Radiation Effects in Breeder Reactor Structural Materials: International Conference June 19-23, 1977, Camelback Inn, Scottsdale, Arizona (1977); p. 1023.Google Scholar
Brailsford, A. and Bullough, R.: The rate theory of swelling due to void growth in irradiated metals. J. Nucl. Mater. 44, 121 (1972).Google Scholar
Dunlop, A., Rullier-Albenque, F., Jaouen, C., Templier, C., and Davenas, J.: Materials under Irradiation (Trans Tech Publication, Les Ulis, France, 1993).Google Scholar
Maydet, S. and Russel, K.: Precipitate stability under irradiation: Point defect effects. J. Nucl. Mater. 64, 101 (1977).Google Scholar
Sizmann, R.: The effect of radiation upon diffusion in metals. J. Nucl. Mater. 69, 386–412 (1978).Google Scholar
Berge, P., Pomeau, Y., and Vidal, C.: L’ordre dans le chaos (Hermann Paris, Paris, France, 1984).Google Scholar
Somorjai, R.: Physical Chemistry, Vol. XI-B (Academic Press, New York, 1975).Google Scholar
Cross, M.C. and Hohenberg, P.C.: Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993).Google Scholar
Sikka, V. and Moteff, J.: Superlattice of voids in neutron-irradiated tungsteno. J. Appl. Phys. 43, 4942 (1972).CrossRefGoogle Scholar
Beauford, M., Vallet, M., Nicolai, J., and Bardot, J.: In situ evolution of he bubbles in sic under irradiation. J. Appl. Phys. 118, 205904 (2015).CrossRefGoogle Scholar
Walgraef, D.: Spatio-Temporal Pattern Formation (With Examples in Physics, Chemistry and Materials Science) (Springer-Verlag, New York, New York, 1996).Google Scholar
Pomeau, Y. and Manneville, P.: Stability and fluctuation of a spatially periodic convective flow. J. Phys., Lett. 40, 609–612 (1979).Google Scholar
Coullet, P., Emilsson, K., and Plaza, F.: Instabilities in Nonequilibrium Structures III (Kluwer, Dorrecht, 1991).Google Scholar
Le Bellac, M., Mortessagne, F., and Batrouni, G.: Equilibrium and Non Equilibrium Statistical Thermodynamics (Cambridge University Press, Cambridge, United Kingdom, 2010).Google Scholar
Martin, G.: Phase stability under irradiation: Ballistic effects. Phys. Rev. B 30, 53 (1984).Google Scholar
Bergersen, B. and Racz, Z.: Dynamical generation of long-range interactions: Random levy flights in kinetic ising and spherical models. Phys. Rev. Lett. 67, 3047 (1991).Google Scholar
Huston, E.L., Cahn, J.W., and Hilliard, J.E.: Spinodal decomposition during continuous cooling. Acta Metall. 14, 1053 (1966).Google Scholar
Adda, Y., Beyeler, M., and Brebec, G.: Monte Carlo simulation of phase separation in chemically reactive binary mixture. Thin Solid Films 25, S28 (1975).Google Scholar
Tsaur, B., Lau, S., and Mayer, J.: Continuous series of metastable agcu solid solutions formed by ion beam mixing. Appl. Phys. Lett. 36, 823 (1980).CrossRefGoogle Scholar
Chen, L. and Khatchaturyan, A.: Dynamics of simultaneous orderring and phase separation and effect of long range coulomb interactions. Phys. Rev. Lett. 70, 1477 (1993).Google Scholar
Demange, G., Luneville, L., Pontikis, V., and Simeone, D.: Prediction of irradiation induced microstructures using a multiscale method coupling atomistic and phase field modeling: Application to the agcu model alloy. J. Appl. Phys. 121, 125108–125122 (2017).CrossRefGoogle Scholar
Bray, A.J.: Theory of phase-ordering kinetics. J. Adv. Phys. 43, 357–459 (1994).Google Scholar
Luneville, L., Mallick, K., Pontikis, V., and Simeone, D.: Patterning in systems driven by non local external forces. Phys. Rev. E 94, 052126 (2016).Google Scholar
Ohta, T. and Kawasaki, K.: Equilibrium morphology of block copolymer melts. Macromolecules 19, 2621 (1986).Google Scholar
Simeone, D., Demange, G., and Luneville, L.: Disrupted coarsening in complex Cahn–Hilliard dynamics. Phys. Rev. E 88, 032116 (2013).Google Scholar
Opplestrup, T., Bulatov, V., Gilmer, G., Kalos, M., and Sadigh, B.: First passage monte-carlo algorithm: Diffusion without all the hops. Phys. Rev. Lett. 97, 230602 (2006).Google Scholar
Biron, I.: Thesis: Corsening Kinetics Induced by Irradiation in Pb Glasses (Orsay University, Paris, France, 1988).Google Scholar