Freezing on a sphere

• Published in: Nature (London) 2018-02, Vol.554 (7692), p.346-350
• Main Authors: Guerra, Rodrigo E., Kelleher, Colm P., Hollingsworth, Andrew D., Chaikin, Paul M.
• Format: Article
• Language: English
• Subjects: 639/301/923/916; 639/301/923/966; 639/766/530/2795; Broken symmetry; Capsid - chemistry; Crystal defects; Crystallization; Crystals; Curvature; Defects; Design defects; Freezing; Humanities and Social Sciences; Hydrophobic and Hydrophilic Interactions; Icosahedral phase; letter; Microspheres; Models, Chemical; multidisciplinary; Order parameters; Phase transitions; Physics research; Science; Simulation; Spheres (Geometry); Surface Properties; Symmetry; Topology; Vortices
• ISSN: 0028-0836; 1476-4687
• DOI: 10.1038/nature25468

Freezing on a spherical surface is shown to proceed by the sequestration of defects into 12 icosahedrally coordinated ‘seas’ that enable the formation of a crystalline ‘continent’ with long-range orientational order. Crystal healing Crystallization of a liquid in two dimensions can be understood as arising from the annihilation of pairs of structural defects as the temperature is lowered. But if the surface is curved, some defects must always be present. For example, the ordered hexagons on the surface of a football require 12 additional pentagons ('defects') to complete the sphere. Given the impossibility of eliminating all defects on a curved surface, can crystallization from a liquid state even take place in such a system? The answer is yes, according to Rodrigo Guerra et al . Using a combination of experiments and simulations of charged colloidal particles bound to the surface of a sphere, they observe how order emerges from an initial liquid-like state as the system freezes. In particular, they note how the defects are gradually forced into 12 isolated pockets on the surface, analogous to the topology-preserving pentagonal defects on a football. The best understood crystal ordering transition is that of two-dimensional freezing, which proceeds by the rapid eradication of lattice defects as the temperature is lowered below a critical threshold 1 , 2 , 3 , 4 . But crystals that assemble on closed surfaces are required by topology to have a minimum number of lattice defects, called disclinations, that act as conserved topological charges—consider the 12 pentagons on a football or the 12 pentamers on a viral capsid 5 , 6 . Moreover, crystals assembled on curved surfaces can spontaneously develop additional lattice defects to alleviate the stress imposed by the curvature 6 , 7 , 8 . It is therefore unclear how crystallization can proceed on a sphere, the simplest curved surface on which it is impossible to eliminate such defects. Here we show that freezing on the surface of a sphere proceeds by the formation of a single, encompassing crystalline ‘continent’, which forces defects into 12 isolated ‘seas’ with the same icosahedral symmetry as footballs and viruses. We use this broken symmetry—aligning the vertices of an icosahedron with the defect seas and unfolding the faces onto a plane—to construct a new order parameter that reveals the underlying long-range orientational order of the lattice. The effects of geometry on crystallization could be taken into