Read--Shockley formula for a general Bravais lattice in two dimensions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918461229236224 |
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| author | Scardia, Lucia Tolotti, Edoardo Giovanni |
| author_facet | Scardia, Lucia Tolotti, Edoardo Giovanni |
| contents | In this note we consider a two-dimensional semi-discrete dislocation energy and propose a simple and physically motivated construction for the grain boundary between two crystal grains with a small orientation difference. In the case of a general Bravais lattice, the energy of this construction matches the logarithmic scaling predicted by Read and Shockley. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_20287 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Read--Shockley formula for a general Bravais lattice in two dimensions Scardia, Lucia Tolotti, Edoardo Giovanni Analysis of PDEs 74C15, 58K45 In this note we consider a two-dimensional semi-discrete dislocation energy and propose a simple and physically motivated construction for the grain boundary between two crystal grains with a small orientation difference. In the case of a general Bravais lattice, the energy of this construction matches the logarithmic scaling predicted by Read and Shockley. |
| title | Read--Shockley formula for a general Bravais lattice in two dimensions |
| topic | Analysis of PDEs 74C15, 58K45 |
| url | https://arxiv.org/abs/2604.20287 |