Fig. 2 Structure and PMFT isosurfaces for optimal shapes in six target structures: β-Mn, BCC, FCC, β-W, SC, and diamond. Structure and PMFT isosurfaces.

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Fig. 2 Structure and PMFT isosurfaces for optimal shapes in six target structures: β-Mn, BCC, FCC, β-W, SC, and diamond. Structure and PMFT isosurfaces for optimal shapes in six target structures: β-Mn, BCC, FCC, β-W, SC, and diamond. (A to F) Structural coordination (global: BCC, FCC, SC, diamond; local: β-Mn, β-W) and PMFT isosurfaces at free energy values of 1.4 kBT (light gray) and 0.7 kBT (pink) above the minimum value for an optimal but unsymmetrized convex polyhedron (top) and for an optimal symmetry-restricted polyhedron (bottom). PMFT isosurfaces indicate that the emergence of particle faceting corresponds with entropic valence localized at particle facets that preferentially align along crystal lattice directions. PMFT isosurfaces for symmetry-restricted polyhedra retain valence-lattice correspondence. Yina Geng et al. Sci Adv 2019;5:eaaw0514 Copyright © 2019 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).