caa a22 4500 605515778 CHVBK 20210128100711.0 cr unu---uuuuu 210128e20151001xx s 000 0 eng 10.1007/s00205-015-0862-1 doi (NATIONALLICENCE)springer-10.1007/s00205-015-0862-1 Face-Centered Cubic Crystallization of Atomistic Configurations [Elektronische Daten] [L. Flatley, F. Theil] 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. Springer-Verlag Berlin Heidelberg, 2015 Flatley L. Mathematics Institute, University of Warwick, CV47AL, Coventry, UK aut Theil F. Mathematics Institute, University of Warwick, CV47AL, Coventry, UK aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/1(2015-10-01), 363-416 0003-9527 218:1<363 2015 218 205 https://doi.org/10.1007/s00205-015-0862-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-015-0862-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Flatley L. Mathematics Institute, University of Warwick, CV47AL, Coventry, UK aut NATIONALLICENCE 700 1- Theil F. Mathematics Institute, University of Warwick, CV47AL, Coventry, UK aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 218/1(2015-10-01), 363-416 0003-9527 218:1<363 2015 218 205