Face-Centered Cubic Crystallization of Atomistic Configurations
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| 005 | 20210128100711.0 | ||
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| 008 | 210128e20151001xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-015-0862-1 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-015-0862-1 | ||
| 245 | 0 | 0 | |a Face-Centered Cubic Crystallization of Atomistic Configurations |h [Elektronische Daten] |c [L. Flatley, F. Theil] |
| 520 | 3 | |a We address the question of whether three-dimensional crystals are minimizers of classical many-body energies. This problem is of conceptual relevance as it presents a significant milestone towards understanding, on the atomistic level, phenomena such as melting or plastic behavior. We characterize a set of rotation- and translation-invariant two- and three-body potentials V 2, V 3 such that the energy minimum of $$\frac{1}{\#Y}E(Y) = \frac{1}{\# Y} \left(2\sum_{\{y,y'\} \subset Y}V_2(y, y') + 6\sum_{\{y,y',y''\} \subset Y} V_3(y,y',y'')\right)$$ 1 # Y E ( Y ) = 1 # Y 2 ∑ { y , y ′ } ⊂ Y V 2 ( y , y ′ ) + 6 ∑ { y , y ′ , y ′ ′ } ⊂ Y V 3 ( y , y ′ , y ′ ′ ) over all $${Y \subset \mathbb{R}^3}$$ Y ⊂ R 3 , #Y =n, converges to the energy per particle in the face-centered cubic (fcc) lattice as n tends to infinity. The proof involves a careful analysis of the symmetry properties of the fcc lattice. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2015 | ||
| 700 | 1 | |a Flatley |D L. |u Mathematics Institute, University of Warwick, CV47AL, Coventry, UK |4 aut | |
| 700 | 1 | |a Theil |D F. |u Mathematics Institute, University of Warwick, CV47AL, Coventry, UK |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/1(2015-10-01), 363-416 |x 0003-9527 |q 218:1<363 |1 2015 |2 218 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-015-0862-1 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-015-0862-1 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Flatley |D L. |u Mathematics Institute, University of Warwick, CV47AL, Coventry, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Theil |D F. |u Mathematics Institute, University of Warwick, CV47AL, Coventry, UK |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 218/1(2015-10-01), 363-416 |x 0003-9527 |q 218:1<363 |1 2015 |2 218 |o 205 | ||