Sierpiński-triangle fractal crystals with the C3v point group

Li, Na; Zhang, Xue; Gu, Gaochen; Wang, Hao; Nieckarz, Damian; Szabelski, Paweł; He, Yang; Wang, Yu; Lü, Jing-Tao; Tang, Hao; Peng, Lian‐Mao; Hou, Shimin; Wu, Kai; Wang, Yongfeng

doi:10.1016/j.cclet.2015.08.006

Cited by 45 publications

(47 citation statements)

References 30 publications

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“…First, the widespread application of SAS to deterministic fractals is severely limited by the availability of the suitable samples. Currently, only several materials such as poly-silicone [25], bis-terpyridine macromolecules [26], alkyletene dimers [27], single crystalline silicone [28], Fe atoms, 1,3 -bis (4 -pyridyl) benzene molecules [29], terphenyl molecules [30] or dicarbonitrile molecules [31] have been used to create deterministic structures. However, they can not fulfill the ever increasing requirements for modern technological and industrial applications, such as in stretchable electronics, nano-and microantenna, electrophysiological sensors, or precision monitors and actuators, and thus the types of deterministic materials need to be increased.…”

Section: Future Researchmentioning

confidence: 99%

The structure of deterministic mass and surface fractals: theory and methods of analyzing small-angle scattering data

Cherny

Anitas

Osipov

et al. 2019

Phys. Chem. Chem. Phys.

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Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS data: the fractal dimension, and the lower and upper limits of the fractal range. The self-similarity of deterministic structures allows one to obtain additional characteristics of their spatial structures. The paper considers models which can describe accurately SAS from such structures. The developed models of deterministic fractals offer many advantages in describing fractal systems, including the possibility to extract additional structural information, an analytic description of SAS intensity, and effective computational algorithms. Generalized Cantor fractals and few of its variants are used as basic examples to illustrate the above concepts and to model physical samples with mass, surface, and multi-fractal structures. The differences between the deterministic and random fractal structures in analyzing SAS data are emphasized. Several limitations are identified in order to motivate future investigations of deterministic fractal structures.

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Section: Future Researchmentioning

confidence: 99%

The structure of deterministic mass and surface fractals: theory and methods of analyzing small-angle scattering data

Cherny

Anitas

Osipov

et al. 2019

Phys. Chem. Chem. Phys.

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“…Therefore, ongoing research is carried out to obtain structures with exact self-similar (ESS) properties [13][14][15][16][17][18][19], where an intrinsic pattern repeats itself exactly under scaling. This procedure usually leads to highly symmetric fractal structures, such as Cantor dust, Sierpinski carpet or Menger sponge [20].…”

Section: Introductionmentioning

confidence: 99%

Structural Properties of Vicsek-like Deterministic Multifractals

et al. 2019

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Deterministic nano-fractal structures have recently emerged, displaying huge potential for the fabrication of complex materials with predefined physical properties and functionalities. Exploiting the structural properties of fractals, such as symmetry and self-similarity, could greatly extend the applicability of such materials. Analyses of small-angle scattering (SAS) curves from deterministic fractal models with a single scaling factor have allowed the obtaining of valuable fractal properties but they are insufficient to describe non-uniform structures with rich scaling properties such as fractals with multiple scaling factors. To extract additional information about this class of fractal structures we performed an analysis of multifractal spectra and SAS intensity of a representative fractal model with two scaling factors-termed Vicsek-like fractal. We observed that the box-counting fractal dimension in multifractal spectra coincide with the scattering exponent of SAS curves in mass-fractal regions. Our analyses further revealed transitions from heterogeneous to homogeneous structures accompanied by changes from short to long-range mass-fractal regions. These transitions are explained in terms of the relative values of the scaling factors.

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“…通过对衬底样品温度、分子沉积速率等动力学参数的精确控制, 在吸附限制扩散的影响下, 某些沉积物可以形成枝杈状无序分形结构. 最近人们通过对分子设计、衬底选择、退火温度、退火速率等的调控, 在表面构筑了基于卤键 [9] 、氢键 [13] 、金属有机配位键 [14] 、共价键 [15] 等作用力的有序谢尔宾斯基三角分形结构. 并通过模板法, 在Au(100)重构表面上制备了一维双链分形阵列 [16] , 结合模板法和共组装法, 获得了级数高达五级的谢尔宾斯基三角分形结…”

Section: 引言unclassified

Aperiodic ordered surface structures investigated by scanning tunneling microscopy

et al. 2019

Sci. Sin.-Chim

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Sierpiński-triangle fractal crystals with the C3v point group

Cited by 45 publications

References 30 publications

The structure of deterministic mass and surface fractals: theory and methods of analyzing small-angle scattering data

The structure of deterministic mass and surface fractals: theory and methods of analyzing small-angle scattering data

Structural Properties of Vicsek-like Deterministic Multifractals

Aperiodic ordered surface structures investigated by scanning tunneling microscopy

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