Isochronal Annealing of Electron-Irradiated Tungsten Modelled by CD Method: 1D and 3DModel of SIA Diffusivity


  • M. S. Kondria South Ukrainian National Pedagogical University
  • A. R. Gokhman South Ukrainian National Pedagogical University



cluster dynamics, electron irradiation, isochronal annealing, dimensional of SIA diffusivity


The evolution of the microstructure of tungsten under electron irradiation and post-irradiation annealing has
been modeled using a multiscale approach based on Cluster Dynamics simulations. In these simulations, both
self-interstitials atoms (SIA) and vacancies, carbon atoms isolated or in clusters, are considered. Isochronal annealing has been simulated in carbon free tungsten and tungsten with carbon, focusing on the recovery stages I and II. The carbon atom, single SIA, single vacancy and vacancy clusters with sizes up to four are treated as the mobile pieces. Their diffusivities as well as the energy formation and binding energies are based on the  experimental data and ab initio predictions and some of these parameters have been slightly  adjusted, without modifying the interaction character, on isochronal annealing experimental data. The both models with assumption on 1D as well as 3D dimensionality of diffusivity of SIA are treated. The advantage of the model with 1D diffusivity of SIA is found.


[1] C. C. Fu, J. Dalla Torre, F. Willaime, J.L. Bocquet and A. Barbu, Nature Materials 4, 68 (2005).

[2] T. Amino, K. Arakawa & H. Mori, ... , Scientific Reports 6, 26099 (2016). DOI: 10.1038/srep26099.

[3] N. Castin, A. Bakaev, G. Bonny, A. E. Sand, L. Malerba, D. Terentyev, Journal of nuclear materials 1, 15 (2018).

[4] A. Gokhman, S. Pecko and V. Slugeň, Radiation Effects and Defects in Solids: Incorporating Plasma Science and Plasma Technology 170, 745 (2015).

[5] J. Fikar and R. Schaublin. Nucl. Instr. Methods Phys. Res. B 267(32), 18 (2009).

[6] G. E. Dieter. Mechanical Metallurgy. McGraw-Hill Book Company, London, symmetric edition, 1988.

[7] Y. G. Li, W. H. Zhou, R. H. Ning, L. F. Huang, Z. Zeng1, X. Ju, Commun. Comput. Phys. (11), 1547 (2012).

[8] A. Satta, F. Willaime, and Stefano de Gironcoli, Phys. Rev. B 57, 11184 (1998).

[9] P. M. Derlet, D. Nguyen-Manh, and S. L. Dudarev, Phys. Rev. B 76, 054107 (2007).

[10] Withop Arthur, PhD Thesis, The diffusion of carbon into tungsten, The University of Arizona, (1966).

[11] L. N. Aleksandrov, Zavodskaya Laboratorlya 25, 925 (I960).

[12] J. A. Becker, E. I. Becker, and Re. G. Brandes, J. Appl. Phys. 32, 411 (1961).

[13] C. P. Bushmer, Journal of Material Science 6, 981 (1971).

[14] Yue-Lin Liu, Hong-Bo Zhou, Shuo Jin, Ying Zhang and Guang-Hong Lu, J. Phys.: Condens. Matter 22, 445504 (2010).

[15] W. R. Tyson, W. A. Miller, Surface Science 62, 267 (1977).

[16] C. S. Becquart, C. Domain, U. Sarkar, and et al. J. Nucl. Mater. 403, 75 (2010).

[17] D. Nguyen-Manh, Advanced Materials Research 59, 253 (2009).

[18] Xiang-Shan Kong, Xuebang Wua, Yu-Wei You, C.S. Liu, Q.F. Fang, Jun-Ling Chen, G.-N. Luo, Acta Materialia 66, 172 (2014).

[19] LSODA is part of the ODEPACK provided by Alan C. Hindmarsh 1984 on the CASC server of the Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

[20] Gear.: Numerical Initial Value Problems in Ordinary Differential Equations. Prentice-Hall,Englewood Cliffs, NJ, 1971.

[21] H. H. Neely, D. W. Keeper and A. Sosin, Phys. stat. sol. 28, 675 (1968).



How to Cite

Kondria, M. S., & Gokhman, A. R. (2018). Isochronal Annealing of Electron-Irradiated Tungsten Modelled by CD Method: 1D and 3DModel of SIA Diffusivity. Physics and Chemistry of Solid State, 19(1), 5–13.