[1] J. Huang, Y. Lai, H. Jin, H. Guo, F. Ai, Q. Xing, D. Ross, “Preparation and properties of Zn-Cu alloy for potential stent material”, Materials Engineering and Performance, 29, 6484-6493, 2020.
https://doi.org/10.1007/s11665-020-05167-0
[2] Q. Duan, J. An, H. Mao, D. Liang, H. Li, S. Wang, C. Huang, “Review about the application of fractal theory in the research of packaging materials”, Materials, 14, 860, 2021.
[3] C. Ding, T. Xu, Q. Chen, C. Su, P. Zhao, “Study on the relationship between fractal characteristics and mechanical properties of tensile fracture of reinforced concrete structures”, KSCE Journal of Civil Engineering, 26, 2225-2233, 2022.
https://doi.org/10.1007/s12205-022-0196-0
[4] M. Fakharpour, M. Gholizadeh Arashti, M.T. Musazade Meybodi, “Electrical characterization of zig-zag Aluminum thin films using experimental and theoretical methods”, Journal of Optoelectronical Nanostructures, 6, 25-42, 2021.
[5] L. Chen, S. Lü, W. Guo, J. Li, Wu, “High thermal conductivity of highly alloyed Mg-Zn-Cu alloy and its mechanism”, Journal of Alloys and Compounds, 918, 165614, 2022.
https://doi.org/10.1016/j.jallcom.2022.165614
[6] H. Pan, Y. Ren, H. Fu, H. Zhao, L. Wang, X. Meng, G. Qin, “Recent developments in rare-earth free wrought magnesium alloys having high strength: A review”, Journal of Alloys and Compounds, 663, 321-331, 2016.
https://doi.org/10.1016/j.jallcom.2015.12.057
[7] H. Pan, F. Pan, X. Wang, J. Peng, J. She, C. Zhao, Z. Gao, “High conductivity and high strength Mg-Zn-Cu alloy”, Materials Science and Technology, 30, 759-764, 2014.
https://doi.org/10.1179/1743284713Y.0000000400
[8] M. Fakharpour, G. Taheri, “Fabrication of Al zigzag thin films and evaluation of mechanical and hydrophobic properties”, Applied Physics A, 126, 631, 2020.
https://doi.org/10.1007/s00339-020-03773-2
[9] M. Fakharpour, F. Babaei, H. Savaloni, “Engineering Mn as tetragonal-like helical sculptured thin film for broadband absorption”, Plasmonics, 11, 1579-1587, 2016.
https://doi.org/10.1007/s11468-016-0213-6
[10] M. Fakharpour, M. Gholizadeh Arashti, S. Hesami Tackallou, B. Zamani, “Surface characterization of Al thin film dependent on the substrate using fractal geometry”, Progress in Physics of Applied Materials, 3, 177-183, 2023.
[11] M.H. Karimi Tafti, M. Fakharpour, “Optical Properties of NiO Columnar Nanostructure Prepared by OAD Technique”, Journal of Optoelectronical Nanostructures, 8, 51-67, 2023.
[12] M. Ben Arbia, H. Helal, E. Comini, “Recent Advances in Low-Dimensional Metal Oxides via Sol-Gel Method for Gas Detection”, Nanomaterials, 14, 359, 2024.
https://doi.org/10.3390/nano14040359
[13] V. Golshan, F. Mirjalili, M. Fakharpour, “Self-cleaning surfaces with superhydrophobicity of Ag-TiO2 nanofilms on the floor ceramic tiles”, Glass Physics and Chemistry, 48, 35-42, 2022.
https://doi.org/10.1134/S1087659622010059
[14] E. Montakhab, F. Rashchi, S. Sheibani, “Enhanced photocatalytic activity of TiO2 nanotubes decorated with Ag nanoparticles by simultaneous electrochemical deposition and reduction processes”, Applied Surface Science, 615, 156332, 2023.
https://doi.org/10.1016/j.apsusc.2023.156332
[15] M.L. Personick, A.A. Jallow, G.C. Halford, L.A. Baker, “Nanomaterials Synthesis Discovery via Parallel Electrochemical Deposition”, Chemistry of Materials, 36, 3034, 2024.
https://doi.org/10.1021/acs.chemmater.4c00318
[16] W. Sapota, P. Szczepanik, S. Stach, Z. Wróbel, “Fractal and Multifractal Analyses of the Porosity Degree of Ceramics Used in Biomedicine”, Adv. Sci. Eng. Med., 12, 450-456, 2020.
https://doi.org/10.1166/asem.2020.2546
[17] R. Shakoury, A. Grayeli Korpi, K. Ghosh, Ş. Țălu, S. Rezaee, F. Mwema, M. Mardani, A. Arman, “Stereometric and scaling law analysis of surface morphology of stainless steel type AISI 304 coated with Mn: a conventional and fractal evaluation”, Mater. Res. Express, 6, 116436, 2019.
https://doi.org/1088/2053-1591/ab4aa6
[18] Ş. Țălu, S. Abdolghaderi, E.P. Pinto, R.S. Matos, M. Salerno, “Advanced fractal analysis of nanoscale topography of Ag/DLC composite synthesized by RF-PECVD”, Surface Engineering, 36, 713-719, 2020.
https://doi.org/10.1080/02670844.2019.1710937
[19] M.R.B. Dias, D. Dornelas, W.F. Balthazar, J.A.O. Huguenin, L. da Silva, “Lacunarity study of speckle patterns produced by rough surfaces”, Phys. A, 486, 328-336, 2017.
https://doi.org/10.1016/j.physa.2017.05.022
[20] D. Risović, H. Gebavi, M. Ivanda, “Influence of fractal and lacunar characteristic of a nanostructured substrate on SERS enhancement”, Appl. Surf. Sci., 537, 147915, 2021.
https://doi.org/10.1016/j.apsusc.2020.147915
[21] A. Pander, T. Onishi, A. Hatta, H. Furuta, “Study of self-organized structure in carbon nanotube forest by fractal dimension and lacunarity analysis”, Mater. Charact., 160, 2020.
https://doi.org/10.1016/j.matchar.2019.110086
[22] G.Q. Ramos, R.S. Matos, A. Das, S.T. Kumar, Ş. Țălu, H.D. da Fonseca Filho, “Correlating morphology and multifractal spatial patterns of the leaf surface architecture of Anacardium occidentale L”, Fractal Fract., 6, 320, 2022.
https://doi.org/10.3390/fractalfract6060320
[23] C. Allain, M. Cloitre, “Characterizing the lacunarity of random and determined fractal set”, Physics Review A, 44, 3552-3558, 1991.
https://doi.org/10.1103/PhysRevA.44.3552
[24] ImageJ | World Library - eBooks | Read eBooks, online [WWW Document], 2020. URL
http://www.worldlibrary.in/articles/eng/ImageJ (accessed 11.17.20)
[25] D. Nečas, P. Klapetek, Gwyddion: an open-source software for SPM data analysis, Open Physics, 10, 2012.
https://doi.org/10.2478/s11534-011-0096-2
[26] A.K. Nikumbh, A.V. Nagawade, G.S. Gugale, M.G. Chaskar, P.P. Bakare, “The formation, structural, electrical, magnetic and Mössbauer properties of ferrispinels, Cd1-xNixFe2O4”, Journal of Materials Science, 37, 637-647, 2002.
https://doi.org/10.1023/A:1013790129045
[27] A. Yadav, D. Varshney, “Structural and dielectric properties of copper-substituted Mg-Zn spinel ferrites”, Journal of Superconductivity and Novel Magnetism, 30, 1297-1302, 2017.
https://doi.org/10.1007/s10948-016-3931-2
[28] M. Fakharpour, F. Abrinaei, “Glancing angle deposition of helical manganese oxide nanostructures on the glass substrate and study the optical nonlinearity by Z-scan technique”, Optical Materials, 143, 114219, 2023.
https://doi.org/10.1016/j.optmat.2023.114219
[29] M. Fakharpour, “Fractal and structural analysis of the different sculptured Mn-based nanostructures”, Physics Letters A, 487, 129136, 2023.
https://doi.org/10.1016/j.physleta.2023.129136
[30] B.B. Mandelbrot, “A fractal’s Lacunarity, and how it can be tuned and measured. In Fractals in Biology and Medicine”, edited by T. Nonnenmacher, G. Losa, and E. Weibel, Basel: Birkhauser, 1993, pp. 8-21.
https://doi.org/10.1007/978-3-0348-8501-0_2
[31] E.P. Pinto, M.A. Pires, R.S. Matos, R.R.M. Zamora, R.P. Menezes, R.S. Araújo, T.M. de Souza, “Lacunarity Exponent and Moran Index: A Complementary Methodology to Analyze AFM Images and Its Application to Chitosan Films”, Phys. A Stat. Mech. Appl., 581, 126192, 2021.
https://doi.org/10.1016/j.physa.2021.126192
[32] A. Pander, T. Onishi, A. Hatta, H. Furuta, “Study of self-organized structure in carbon nanotube forest by fractal dimension and lacunarity analysis”, Materials Characterization, 160, 110086, 2020.
https://doi.org/10.1016/j.matchar.2019.110086
[33] A. Das, V. Chawla, R.S. Matos, H.D. da Fonseca Filho, R.P. Yadav, Ş. Țălu, S. Kumar, “Surface microtexture and wettability analysis of quasi two-dimensional (Ti, Al)N thin films using fractal geometry”, Surface and Coatings Technology, 421, 127420, 2021.
https://doi.org/10.1016/j.surfcoat.2021.127420