Senn, W. M. (1998). Equilibrium form of crystals and stable norm. Zeitschrift für angewandte Mathematik und Physik, 49(6), pp. 919-933. Birkhäuser 10.1007/s000330050130
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The equilibrium form of a crystal is the shape which minimizes the total surface tension for a given volume. The surface tension itself is considered to be a function of the orientation of the crystal face within the crystal lattice. This function of orientation is identified with the stable norm on the second homology classes of a Riemannian 3-torus. Minimizing the total surface tension of the crystal leads to an equilibrium form which corresponds to the dual unit ball of the stable norm. We outline the connection between surface tension and stable norm and interpret the differentiability properties of the stable norm in terms of the crystal shape. The differentiability properties, in particular, prove Sohnke's reciprocity law estimating the size of crystal faces.
Item Type: |
Journal Article (Original Article) |
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Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics |
UniBE Contributor: |
Senn, Walter |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
0044-2275 |
Publisher: |
Birkhäuser |
Language: |
English |
Submitter: |
Virginie Sabado |
Date Deposited: |
24 Jan 2023 12:45 |
Last Modified: |
24 Jan 2023 23:27 |
Publisher DOI: |
10.1007/s000330050130 |
BORIS DOI: |
10.48350/177236 |
URI: |
https://boris.unibe.ch/id/eprint/177236 |
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