MODELING OF CLOSE-ORDER FRACTAL STRUCTURES OF METAL-METALLOID ALLOYS WITH CUBIC STRUCTURE

D.B. Sereda; O.S. Baskevуch; B.P. Sereda; I.V. Kryhliyak

doi:10.31489/2025N4/31-38

Authors

DOI:

https://doi.org/10.31489/2025N4/31-38

Keywords:

amorphous state, electrodeposition, modeling, clusters

Abstract

Using methods of mathematical physics, a comprehensive simulation of the short-range order in Fe₈₈P₁₂ and Cr₈₈C₁₂ alloys produced by electrodeposition was carried out. As the initial configuration for modeling, the crystal structure of the base metal was selected. Numerous experimental studies, including X-ray diffraction and electron microscopy analyses, have indicated that in metal-metalloid alloys, surface microstructures predominantly exhibit ellipsoidal morphologies. Based on these experimental observations, it was hypothesized that the macroscopic ellipsoidal formations observed on the alloy surfaces are composed of clusters with relatively simple geometric configurations, such as spheres or ellipsoids. The results of the simulation revealed that these clusters possess characteristic sizes not exceeding 30-50 angstroms, and their vectorial growth predominantly occurs along a single radial direction relative to the substrate surface. This anisotropic growth behavior is attributed to differences in local atomic bonding energy and diffusion kinetics, which drive the preferential alignment of cluster development. Moreover, it was established that the spatial distribution and size uniformity of the clusters significantly influence the overall mechanical and physicochemical properties of the coatings, including hardness, wear resistance, and corrosion stability. The combination of modeling outcomes with empirical data provides valuable insight into the microstructural evolution mechanisms governing electrodeposited metal-metalloid systems. These findings can serve as a basis for optimizing the electrodeposition parameters to tailor the surface structure and enhance the performance characteristics of functional coatings.

References

Danilov F.I., Protsenko V.S., Butyrina T.E., Krasinskii V.A., Baskevich A.S., Kwon S., Lee D.Y. (2011) Electrodeposition of nanocrystalline chromium coatings from Cr(III)-based electrolyte using pulse current. Protection of Metals and Physical Chemistry of Surfaces, 47(5), 598–605. https://doi.org/10.1134/S2070205111050066 DOI: https://doi.org/10.1134/S2070205111050066

Protsenko V.S., Danilov F.I., Gordienko V.O., Baskevich A.S., Artemchuk V.V. (2012) Improving hardness and tribological characteristics of nanocrystalline Cr-C films obtained from Cr(III) plating bath using pulsed electrodeposition. International Journal of Refractory Metals and Hard Materials, 35, 281–283. DOI: https://doi.org/10.1016/j.ijrmhm.2011.10.006

Hu Y. C., Li F.X., Li M.Z., Bai H.Y., Wang W.H. (2015) Five fold symmetry as an indicator of dynamic arrest in metallic glass forming liquids. Nature Communications, 6, 8310. https://doi.org/10.1038/ncomms9310 DOI: https://doi.org/10.1038/ncomms9310

Protsenko V. S., Bobrova L. S., Baskevich A. S., Korniy S. A., Danilov F. I. (2018) Electrodeposition of chromium coatings from a choline chloride based ionic liquid with the addition of water. Journal of Chemical Technology and Metallurgy, 53(5), 906–915. Available at: https://journal.uctm.edu/node/j2018-5/15_17-130_p906-915.pdf

Wu Z.W., et al. (2015) Hidden topological order and its correlation with glass‑forming ability in metallic glasses. Nature Communications, 6, 6035. https://doi.org/10.1038/ncomms7035 DOI: https://doi.org/10.1038/ncomms7035

Ding J., Ma E. (2017) Computational modeling sheds light on structural evolution in metallic glasses and supercooled liquids. Computational Materials, 3, 9. https://doi.org/10.1038/s41524-017-0007-1 DOI: https://doi.org/10.1038/s41524-017-0007-1

Protsenko V. S., Bobrova L.S., Baskevich A.S., Korniy S.A., Danilov F.I. (2018) Electrodeposition of chromium coatings from a choline chloride based ionic liquid with the addition of water. Journal of Chemical Technology and Metallurgy, 53(5), 906–915.

Kuzmann E., Felner I., Sziráki L., Stichleutner S., Homonnay Z., El-Sharif M.R., Chisholm C.U. (2022) Magnetic anisotropy and microstructure in electrodeposited quaternary Sn–Fe–Ni–Co alloys with amorphous character. Materials, 15(9), 3015. https://doi.org/10.3390/ma15093015 DOI: https://doi.org/10.3390/ma15093015

Feng J., Chen P., Li M. (2018) Absence of 2.5 power law for fractal packing in metallic glasses. Journal of Physics: Condensed Matter, 30(25), 255402. https://doi.org/10.1088/1361-648X/aac45f DOI: https://doi.org/10.1088/1361-648X/aac45f

Cheng Y.Q., Ma E. (2011) Atomic-level structure and structure-property relationship in metallic glasses. Progress in Materials Science, 56, 379–473. https://doi.org/10.1016/j.pmatsci.2010.12.002 DOI: https://doi.org/10.1016/j.pmatsci.2010.12.002

Chen D. Z., An Q., Goddard W.A., Greer J.R. (2017) Ordering and dimensional crossovers in metallic glasses and liquids. Physical Review B, 95(2), 024103. https://doi.org/10.1103/PhysRevB.95.024103 DOI: https://doi.org/10.1103/PhysRevB.95.024103

Sereda B.P., Krugliak I.V., Baskevych O.S., Belokon Y.O., Krugliak D.O., Sereda D.B. (2019) The superficial strengthening of construction materials using composition saturant environments [Monograph]. DDTU. 246 p. ISBN 978-966-175-187-2.

Chen D.Z., Wen X.D., Lu J., Wang Q.M., Wang W.H. (2015) Fractal atomic level percolation in metallic glasses. Science, 349(6254), 1306–1310. https://doi.org/10.1126/science.aab1233 DOI: https://doi.org/10.1126/science.aab1233

Ding J., Asta M., Ritchie R.O. (2017) On the question of fractal packing structure in metallic glasses. Proceedings of the National Academy of Sciences, 114(32), 8458–8463. https://doi.org/10.1073/pnas.1705723114 DOI: https://doi.org/10.1073/pnas.1705723114

Ma D., Stoica A.D., Wang X.-L. (2009) Power-law scaling and fractal nature of medium-range order in metallic glasses. Nature Materials, 8(1), 30–34. https://doi.org/10.1038/nmat2340 DOI: https://doi.org/10.1038/nmat2340

Sereda B.P., Baskevych O.S., Krugliak I.V., Sereda D.B., Krugliak D.O. (2023) Obtaining protective coatings using complex functionally active charges and electrodeposition. [Monograph]. DDTU. 190 p. ISBN 978-966-175-244-2

Tang L., Wen T., Wang N., Sun Y., Zhang F., Yang Z., Ho K.-M., Wang C.-Z. (2018) Structural and chemical orders in Ni₆₄.₅Zr₃₅.₅ metallic glass by molecular dynamics simulation. Physical Review Materials, 2(3), 033601. https://doi.org/10.1103/PhysRevMaterials.2.033601 DOI: https://doi.org/10.1103/PhysRevMaterials.2.033601

Wu Z. W., Huo C. W., Li F. X., et al. (2016). Critical scaling of icosahedral medium-range order in CuZr metallic glass-forming liquids. Scientific Reports, 6, 35967. https://doi.org/10.1038/srep35967 DOI: https://doi.org/10.1038/srep35967

Zhuravel I., Mychuda L., Zhuravel Y. (2020) Localization of steel fractures based on the fractal model of their metallographic images. Ukrainian Journal of Mechanical Engineering and Materials Science, 6(2), 12–22. https://doi.org/10.23939/ujmems2020.02.012 DOI: https://doi.org/10.23939/ujmems2020.02.012

Lu Z., Li H., Lei Z., Chang C., Wang X., Lu Z. (2018) The effects of metalloid elements on the nanocrystallization behavior and soft magnetic properties of FeCBSiPCu amorphous alloys. Metals, 8(4), 283. https://doi.org/10.3390/met8040283 DOI: https://doi.org/10.3390/met8040283

Huang B., Ge T. P., Liu G. L., Luan J. (2018) Density fluctuations with fractal order in metallic glasses detected by synchrotron X-ray nano-computed tomography. Acta Materialia, 155, 236–244. https://doi.org/10.1016/j.actamat.2018.05.064 DOI: https://doi.org/10.1016/j.actamat.2018.05.064

MODELING OF CLOSE-ORDER FRACTAL STRUCTURES OF METAL-METALLOID ALLOYS WITH CUBIC STRUCTURE