K(Na,K)Na2[Cu2(SO4)4]: a new highly porous anhydrous sulfate and evaluation of possible ion migration pathways

Alkali copper sulfates form a rapidly developing family of inorganics. Herein, we report synthesis and crystal structure, and evaluate possible ion migration pathways for a novel Na-K-Cu anhydrous sulfate, K(Na,K)Na2[Cu2(SO4)4]. The CuO7 and SO4 polyhedra share common vertices and edges to form [Cu2(SO4)4]4− wide ribbons, which link to each other via common oxygen atoms forming the host part of the structure. Four guest alkali sites are occupied by solely K+, mixture of K+ and Na+, and solely Na+, which agrees well with the size of the cavities. The crystal structure of K(Na,K)Na2[Cu2(SO4)4] contains two symmetry-independent Cu sites with [4+1+(2)] coordination environments. The overall coordination polyhedra of Cu2+ can be considered as `octahedra with one split vertex'. A similar coordination mode was observed also in some other multinary copper sulfates, mostly of the mineral world. These coordination modes were reviewed and five types of CuO7 polyhedra are identified. CuO7 polyhedra are almost restricted to copper sulfates and phosphates. It was found that a larger amount of the smaller SO4 2− and PO4 3− anions can cluster around a single Cu2+ cation; in addition, for such relatively small anions, both mono (κ1) and bidentate (κ2) coordination modes to the Cu2+ are possible. The correlation between crystallographic characteristics and bond valence energies showed that the new copper sulfate framework, [Cu2(SO4)4]4−, contains one interconnected path suitable for Na+ mobility at tolerable activation energies and that K(Na,K)Na2[Cu2(SO4)4] can be considered as a potential candidate for novel Na-ion conductors.

Split-Vertex Technique for Thickness-Accommodation in Origami-Based Mechanisms

A novel thickness-accommodation technique for origami based mechanisms is introduced. This technique modifies a zero-thickness pattern by splitting each vertex along the minor folds into a system of two vertices. The modified fold pattern then has thickness applied to it and the resulting mechanism is kinematically equivalent to the modified fold pattern. Origami patterns that are rigid-foldable and only have two panels that stack between folds are utilized in the technique. The technique produces thick origami mechanisms where all panels lie in a plane in the unfolded state without any holes or protrusions and maintain a single degree of freedom. Steps for synthesizing split-vertex mechanisms are presented and examples of split-vertex mechanisms are shown. Advantages and potential applications of the technique are discussed.