Screw symmetry in columnar crystals

Abstract

We show that the optimal packing of hard spheres in an infinitely long cylinder yields structures characterised by a screw symmetry. Each packing can be assembled by stacking a basic unit cell ad infinitum along the length of the cylinder with each subsequent unit cell rotated by the same twist angle with respect to the previous one. In this paper we quantitatively describe the nature of this screw operation for all such packings in the range 1 ≤ D/d ≤ 2.715 and also briefly discuss their helicity.

Corrected Article: Simulation and observation of line-slip structures in columnar structures of soft spheres [Phys. Rev. E 96, 012610 (2017)]

“…is the volume of the unit cell of the soft-sphere packing (for the chosen p and D/d) and V 0 is the volume of the corresponding hard-sphere structure. In the case of uniform structures, the volume of the unit cell in the hard-sphere case has a unique value [17]. However, for the line-slip structures this is not the case (since the length of the unit cell depends on D/d) and instead we compare against the smallest volume of the unit cell for a given hard-sphere arrangement of this type [17].…”

“…Columnar structures arise in their most elementary form when we seek the densest packing of hard spheres inside (or on the surface) of a circular cylinder [14][15][16][17][18][19][20]. A wide range of structures have been identified and tabulated [16], depending on the ratio of cylinder diameter D to sphere diameter d.…”

Plastic deformation of tubular crystals by dislocation glide

“…1(c) [17]. The same is true for packings of spheres that are constrained to lie in contact with a solid cylinder, as the sphere centers all sit at a fixed radius R from the center line [12,18,19]. The relative stability of uniform rhombic packings versus line-slip packings has been shown recently to depend on the softness of the interparticle potential [12].…”

Densest-Packed Columnar Structures of Hard Spheres: An Investigation of the Structural Dependence of Electrical Conductivity

“…Prominent examples include the application of the face-centered cubic (fcc) and hexagonal close-packed (hcp) structures as models for bulk crystal structures of solids [4] and the application of random close packings as models for bulk amorphous structures of liquids [3,6]. In contrast to these examples for bulk systems, the past few decades have seen an uprising interest in the packings of particles in confined settings, such as those of particles confined within a two-dimensional box [7,8], within a parallel strip [9][10][11][12][13][14], within a spherical container [15,16], within a cylindrical container [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36], onto a cylindrical surface [37], between parallel plates [38][39][40][41][42][43][44][45][46], within a wedge cell [47,48], or within a flexible conta...…”