We show that near densest packing the perturbations of the hexagonal close packed (hcp) structure yield higher entropy than perturbations of any other densest packing. The difference between the various structures shows up in the correlations between motions of nearest neighbors. In the hcp structure random motion of each sphere impinges slightly less on the motion of its nearest neighbors than...

The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a solid to become unstable when its stress exceeds a critical value. Previous analyses of the surface instability have assumed two-dimensional plane-strain cond...

Three-dimensional periodic complex structures are encountered in various soft matter systems such as liquid crystals, block-copolymer phases and the related nano-structured materials. Here, we review several well-defined topologies: two-dimensional hexagonal phase, three-dimensional packing of spheres, tetrahedral close packing (tcp) bi-continuous and tri-continuous cubic phases. We illustrate ...

In this paper, we report the electrochemical fabrication of highly ordered Au nanowire arrays within hexagonal close-packed nanochannel alumina (NCA) templates with pore diameters ranging from 35 nm to 100 nm. The observations of TEM, SAED, and HRTEM show that single crystal Au nanowires have been obtained within the templates with 45 nm diameters. The growth mechanism of the single crystal Au ...

This article is an introduction to anodization of aluminum, which is a subject of electrochemistry. Anodization of aluminum under a controlled electrochemical condition yields ordered porous alumina with a close-packed hexagonal array of cylindrical nanochannels. The diameter, density, and aspect ratio of pores can be tightly controlled by varying the anodization condition, which makes the poro...

The development of a twinned microstructure in hexagonal close-packed rolled magnesium compressed in the in-plane direction has been monitored in situ with neutron diffraction. The continuous conversion of the parent to daughter microstructure is tracked through the variation of diffraction peak intensities corresponding to each. Approximately 80% of the parent microstructure twins by 8% compre...

Polymorphism in formate-based dense metal-organic frameworks with the general formula ABX3 is predicted by quantum chemical calculations and confirmed experimentally. In particular [NH3NH2]Zn(HCOO)3 crystallizes in two different polymorphs, a perovskite-like framework and a chiral structure with hexagonal channels. A detailed thermodynamic analysis reveals that both structures are very close in...

Fujifilm’s third generation full field digital mammography (FFDM) system, ASPIRE Cristalle, is based on Fujifilm’s unique and innovative technologies that achieve optimum image quality at very low patient dose. These outcomes are made possible by a new detector technology that uses a hexagonal close pattern (HCP) architecture, coupled with analytical and adaptive image processing that automatic...

Group theory arguments have demonstrated that a general odd parity order parameter cannot have line nodes in the presence of spin-orbit coupling. In this paper, it is shown that these arguments do not hold on the kz = π/c zone face of a hexagonal close packed lattice. In particular, three of the six odd parity representations vanish identically on this face. This has potential relevance to the ...

The Onsager reaction-field (ORF) theory is extended to apply to three-dimensional Bravais lattices with a basis. The ORF calculation is used to predict the critical temperature for classical Ising, XY, and Heisenberg magnetic models, in particular, on diamond and hexagonal close packed lattices. Results are compared with series extrapolations and other theoretical approaches where available. Fo...