In this study, three different materials (pure tungsten and two tungsten alloys with Fe and Ni dopants), which have been irradiated with a high-temperature deuterium plasma of 20, 25 and 100 plasma shots, are considered. The multifractal characteristics obtained from SEM images are then compared for the same specimens by analysing the distribution of defects and non-defects (non-damaged areas). A valid tendency was found that the brighter the original input image, the more accurate the results obtained when examining a non-damaged surface using multifractal characteristics.
1. Loarte, A., Saibene, G., Sartori, R., Riccardo, V., Andrew, P., Paley, J. et al. Transient heat loads in current fusion experiments, extrapolation to ITER and consequences for its operation. Phys. Scr., 2007, T128, 222–228.
https://doi.org/10.1088/0031-8949/2007/T128/043
2. Pitts, R. A., Bonnin, X., Escourbiac, F., Frerichs, H., Gunn, J. P., Hirai, T. et al. Physics basis for the first ITER tungsten divertor. Nucl. Mater. Energy, 2019, 20, 100696.
https://doi.org/10.1016/j.nme.2019.100696
3. Hirai, T., Barabash, V., Escourbiac, F., Durocher, A., Ferrand, L., Komarov, V. and Merola, M. ITER divertor materials and manufacturing challenges. Fusion Eng. Des., 2017, 125, 250–255.
https://doi.org/10.1016/j.fusengdes.2017.07.009
4. Huber, A., Arakcheev, A., Sergienko, G., Steudel, I., Wirtz, M., Burdakov, A. V. et al. Investigation of the impact of transient heat loads applied by laser irradiation on ITER-grade tungsten. Phys. Scr., 2014, T159, 014005.
https://doi.org/10.1088/0031-8949/2014/T159/014005
5. Paju, J., Väli, B., Laas, T., Shirokova, V., Laas, K., Paduch, M. et al. Generation and development of damages in double forged tungsten in different combined regimes of irradiation with extreme heat loads. J. Nucl. Mater., 2017, 495, 91–102.
https://doi.org/10.1016/j.jnucmat.2017.07.042
6. Herashchenko, S. S., Girka, O. I., Surovitskiy, S. V., Makhlai, V. A., Malykhin, S. V., Myroshnyk, M. O. et al. Effect of sequential steady-state and pulsed hydrogen plasma loads on structure of textured tungsten samples. Nucl. Instrum. Methods Phys. Res. Sect. B: Beam Interact. Mater. At., 2019, 440, 82–87.
https://doi.org/10.1016/j.nimb.2018.12.010
7. Umstadter, K. R., Rudakov, D. L., Wampler, W., Watkins, J. G. and Wong, C. P. C. Effect of ELMs on deuterium-loaded-tungsten plasma facing components. J. Nucl. Phys. Mater., 2011, 415 (Suppl.), S83–S86.
https://doi.org/10.1016/j.jnucmat.2010.11.104
8. Yajima, M., Ohno, N., Kajita, S., De Temmerman, G., Bystrov, K., Bardin, S. et al. Investigation of arcing on fiber-formed nanostructured tungsten by pulsed plasma during steady state plasma irradiation. Fusion Eng. Des., 2016, 112, 156–161.
https://doi.org/10.1016/j.fusengdes.2016.07.026
9. Lemahieu, N., Linke, J., Pintsuk, G., Van Oost, G., Wirtz, M. and Zhou, Z. Performance of yttrium doped tungsten under ’edge localized mode’-like loading conditions. Phys. Scr., 2014, T159, 014035.
https://doi.org/10.1088/0031-8949/2014/T159/014035
10. Tan, X., Luo, L., Chen, H., Zhu, X., Zan, X., Luo, G. et al. Mechanical properties and microstructural change of W–Y2O3alloy under helium irradiation. Sci. Rep., 2015, 5, 12755.
https://doi.org/10.1038/srep12755
11. Shirokova, V., Laas, T., Ainsaar, A., Priimets, J., Ugaste, Ü., Väli, B. et al. Armor materials’ behavior under repetitive dense plasma shots. Phys. Scr., 2014, T161, 014045.
https://doi.org/10.1088/0031-8949/2014/T161/014045
12. Shirokova, V., Laas, T., Ainsaar, A., Priimets, J., Ugaste, Ü., Demina, E. V. et al. Comparison of damages in tungsten and tungsten doped with lanthanum-oxide exposed to dense deuterium plasma shots. J. Nucl. Phys., 2013, 435, 181–188.
https://doi.org/10.1016/j.jnucmat.2012.12.027
13. Zhang, X. and Yan, Q. Morphology evolution of La2O3 and characteristic in W-La2O3 alloy under transient heat loading. J. Nucl. Phys., 2014, 451, 283–291.
https://doi.org/10.1016/j.jnucmat.2014.04.001
14. Vilémová, M., Pala, Z., Jäger, A., Matějíček, J., Chernyshova, M., Kowalska-Strzęciwilk, E. et al. Evaluation of surface, microstructure and phase modifications on various tungsten grades induced by pulsed plasma loading. Phys. Scr., 2016, 91, 034003.
https://doi.org/10.1088/0031-8949/91/3/034003
15. Makhlai, V. A., Garkusha, I. E., Linke, J., Malykhin, S. V., Aksenov, N. N., Byrka, O. V. et al. Damaging of tungsten and tungsten–tantalum alloy exposed in ITER ELM-like conditions. Nucl. Mater. Energy, 2016, 9, 116–122.
https://doi.org/10.1016/j.nme.2016.04.001
16. Luo, L., Shi, J., Lin, J., Zan, X., Zhu, X., Xu, Q. and Wu, Y. Microstructure and performance of rare earth element-strengthened plasma-facing tungsten material. Sci. Rep., 2016, 6, 32701.
https://doi.org/10.1038/srep32701
17. Nogami, S., Guan, W. H., Hattori, T., James, K. and Hasegawa, A. Improved structural strength and lifetime of monoblock divertor targets by using doped tungsten alloys under cyclic high heat flux loading. Phys. Scr., 2017, T170, 014011.
https://doi.org/10.1088/1402-4896/aa864d
18. Nogami, S., Pintsuk, G., Matsui, K., Watanabe, S., Wirtz, M., Loewenhoff, T. and Hasegawa, A. Thermal shock behavior of potassium doped and rhenium added tungsten alloys. Phys. Scr., 2020, T171, 014020.
https://doi.org/10.1088/1402-4896/ab3dcc
19. Martsepp, M., Laas, T., Laas, K., Priimets, J., Tõkke, S. and Mikli, V. Dependence of multifractal analysis parameters on the darkness of a processed image. Chaos, Solitons and Fractals, 2022, 156, 111811.
https://doi.org/10.1016/j.chaos.2022.111811
20. Tõkke, S., Laas, T., Priimets, J., Mikli, V. and Antonov, M. Impact of pulsed deuterium plasma irradiation on dual-phase tungsten alloys. Fus. Engin. Des., 2021, 164, 112215.
https://doi.org/10.1016/j.fusengdes.2020.112215
21. Soesoo, A., Kalda, J., Bons, P., Urtson, K. and Kalm, V. Fractality in geology: a possible use of fractals in the studies of partial melting processes. Proc. Estonian Acad. Sci. Geology, 2004, 53(1), 13–27.
https://doi.org/10.3176/geol.2004.1.02
22. Makowiec, D., Rynkiewicz, A., Gałaska, R., Wdowczyk-Szulc, J. and Żarczyńska-Buchowiecka, M. Reading multifractal spectra: Aging by multifractal analysis of heart rate. Europhys. Lett., 2011, 94(6), 68005.
https://doi.org/10.1209/0295-5075/94/68005
23. Frankhauser, P., Tannier, C., Vuidel, G. and Houot, H. An integrated multifractal modelling to urban and regional planning. Comput. Environ. Urban Syst., 2018, 67, 132–146.
https://doi.org/10.1016/j.compenvurbsys.2017.09.011
24. Rendón de la Torre, S., Kalda, J., Kitt, R. and Engelbrecht, J. Fractal and multifractal analysis of complex networks: Estonian network of payments. Europ. Phys. J. B., 2017, 90(12), 1–13.
https://doi.org/10.1140/epjb/e2017-80214-5
25. Jafari, A., Tahani, K., Dastan, D., Asgary, S., Shi, Z., Yin, X. T. et al. Ion implantation of copper oxide thin films; statistical and experimental results. Surf. Interfaces, 2020, 18, 100463.
https://doi.org/10.1016/j.surfin.2020.100463
26. Ţălu, Ş., Contreras-Bulnes, R., Morozov, I. A., Rodríguez-Vilchis, L. E. and Montoya-Ayala, G. Surface nanomorphology of human dental enamel irradiated with an Er:YAG laser. Laser Phys., 2016, 26, 025601.
https://doi.org/10.1088/1054-660X/26/2/025601
27. Kajita, S., Yoshida, N., Ohno, N. and Tsuji, Y. Growth of multifractal tungsten nanostructure by He bubble induced directional swelling. New J. Phys., 2015, 17, 043038.
https://doi.org/10.1088/1367-2630/17/4/043038
28. Das, A., Yadav, R. P., Chawla, V., Kumar, S., Ţălu, Ş., Pinto, E. P. and Matos, R. S. Analyzing the surface dynamics of titanium thin films using fractal and multifractal geometry. Mater. Today Commun., 2021, 27, 102385.
https://doi.org/10.1016/j.mtcomm.2021.102385
29. Budaev, V. P., Takamura, S., Ohno, N. and Masuzaki S. Superdiffusion and multifractal statistics of edge plasma turbulence in fusion devices. Nucl. Fusion, 2006, 46, S181.
https://doi.org/10.1088/0029-5515/46/4/S10
30. Ţălu, Ş., Matos, R. S., Pinto, E. P., Rezaee, S. and Mardani, M. Stereometric and fractal analysis of sputtered Ag-Cu thin films. Surf. Interfaces, 2020, 21, 100650.
https://doi.org/10.1016/j.surfin.2020.100650
31. Shakoury, R., Rezaee, S., Mwema, F., Luna, C., Ghosh, K., Jurečka, S. et al. Multifractal and optical bandgap characterization of Ta2O5 thin films deposited by electron gun method. Opt. Quantum Electron., 2020, 52, 95.
https://doi.org/10.1007/s11082-019-2173-5
32. Shakoury, R., Arman, A., Ţălu, Ş., Ghosh, K., Rezaee, S., Luna, C. et al. Optical properties, microstructure, and multifractal analyses of ZnS thin films obtained by RF magnetron sputtering. J. Mater. Sci. Mater. Electron., 2020, 31(7), 5262–5273.
https://doi.org/10.1007/s10854-020-03086-3
33. Jelinek, H. F., Milošević, N. T., Karperien, A. and Krstonošić, B. Box-counting and multifractal analysis in neuronal and glial classification. In Advances in Intelligent Systems and Computing (Dumitrache, I., ed.). Springer, Berlin, Heidelberg, 2013, 177–189.
https://doi.org/10.1007/978-3-642-32548-9_13
34. Fu, H., Wang, W., Chen, X., Pia, G. and Li, J. Fractal and multifractal analysis of fracture surfaces caused by hydrogen embrittlement in high-Mn twinning/transformation-induced plasticity steels. Appl. Surf. Sci., 2019, 470, 870–881.
https://doi.org/10.1016/j.apsusc.2018.11.179
35. Tang, W. and Wang, Y. Fractal characterization of impact fracture surface of steel. Appl. Surf. Sci., 2012, 258(10), 4777–4781.
https://doi.org/10.1016/j.apsusc.2012.01.091
36. Martsepp, M., Laas, T., Laas, K., Väli, B., Gribkov, V. A., Paduch, M. and Matulka, R. Multifractal analysis of plasma irradiated tungsten alloy samples. AIP Conf. Proc., 2019, 2164, 100005.
https://doi.org/10.1063/1.5130842
37. Martsepp, M., Laas, T., Laas, K., Priimets, J., Mikli, V. and Antonov, M. Multifractal analysis of high-temperature plasma irradiated tungsten surfaces. Surf. Topogr.: Metrol. Prop., 2021, 9, 035030.
https://doi.org/10.1088/2051-672X/ac1dc3
38. Ţălu, Ş., Guzzo, P. L., Astinchap, B. and Ghanbaripour, H. Multifractal analysis of ultrasonically machined surfaces of cylindrical quartz crystals: the effect of the abrasive grits. Surf. Topogr.: Metrol. Prop., 2021, 9, 045051.
https://doi.org/10.1088/2051-672x/ac459c
