| _version_ | 1866901786551386112 |
|---|---|
| author | Stephan, Schäperklaus |
| author_facet | Stephan, Schäperklaus |
| contents | <p> Self-organization is a fundamental process in nature where ordered structures<br> emerge from disordered components without external direction. This paper exam<br>ines the phenomenon of self-organizing crystal patterns across dimensional scales, fo<br>cusing particularly on two-dimensional graphene formations and three-dimensional<br> snowflakes. By analyzing the thermodynamic and kinetic factors that drive pattern<br> formation, we identify remarkable similarities in the underlying mechanisms despite<br> dimensional differences. The research reveals that pattern diversity in both systems<br> is governed by similar principles of edge kinetics, surface diffusion, and environmen<br>tal conditions. Quantitative analysis shows that graphene dendritic crystals exhibit<br> fractal dimensions averaging 1.76, comparable to classical Diffusion-Limited Aggre<br>gation models, while dendritic snowflakes follow similar mathematical principles in<br> three dimensions. These findings suggest universal principles of self-organization<br> that transcend dimensionality and specific materials, with significant implications<br> for designing novel materials with controllable morphologies and properties.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15791929 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Self-Organizing Crystal Patterns: From Snowflakes to Graphene Stephan, Schäperklaus self organization Crystal growth snowflakes Graphene Graphite/analysis pattern formation Materials science Materials Science Materials Science/education Materials Science/methods material science Phase Transition <p> Self-organization is a fundamental process in nature where ordered structures<br> emerge from disordered components without external direction. This paper exam<br>ines the phenomenon of self-organizing crystal patterns across dimensional scales, fo<br>cusing particularly on two-dimensional graphene formations and three-dimensional<br> snowflakes. By analyzing the thermodynamic and kinetic factors that drive pattern<br> formation, we identify remarkable similarities in the underlying mechanisms despite<br> dimensional differences. The research reveals that pattern diversity in both systems<br> is governed by similar principles of edge kinetics, surface diffusion, and environmen<br>tal conditions. Quantitative analysis shows that graphene dendritic crystals exhibit<br> fractal dimensions averaging 1.76, comparable to classical Diffusion-Limited Aggre<br>gation models, while dendritic snowflakes follow similar mathematical principles in<br> three dimensions. These findings suggest universal principles of self-organization<br> that transcend dimensionality and specific materials, with significant implications<br> for designing novel materials with controllable morphologies and properties.</p> |
| title | Self-Organizing Crystal Patterns: From Snowflakes to Graphene |
| topic | self organization Crystal growth snowflakes Graphene Graphite/analysis pattern formation Materials science Materials Science Materials Science/education Materials Science/methods material science Phase Transition |
| url | https://doi.org/10.5281/zenodo.15791929 |