Stephen T. Hyde

Morphological influence of magnesium and organic additives on the precipitation of calcite

Calcium carbonate was precipitated from saturated solutions of calcium bicarbonate in the presence of magnesium and organic additives in order to investigate the effect of Mg-incorporation on calcite morphologies. A range of concentrations of Mg and organic additives were investigated, and the structure, composition and morphologies of the crystals were determined using X-ray diffraction and electron microscopy. The action of the organic additives in Mg-free solutions was highly specific, producing elongated single calcite crystals. A much wider range of calcite morphologies was observed in the presence of both Mg and organic additives, and a transition from single crystal to aggregates occurred on increasing the Mg concentration. The MgCO3 content of the crystals increased with the solution Mg concentration, but showed little correlation with the organic additive concentration. Single crystals of magnesian calcite containing up to approximately 10% MgCO3 were prepared, and typically exhibited rounded faces and edges. The polycrystalline aggregates had morphologies ranging from dumbbells to spheres and occluded up to about 22% MgCO3. The experiments suggest that Mg2+ ions act in combination with organic additives to affect calcite morphologies by mechanisms such as adsorption on specific crystal faces which inhibits growth, and by altering the calcite nucleation and growth processes.

Morphogenesis of Self-Assembled Nanocrystalline Materials of Barium Carbonate and Silica

The precipitation of barium or strontium carbonates in alkaline silica-rich environments leads to crystalline aggregates that have been named silica/carbonate biomorphs because their morphology resembles that of primitive organisms. These aggregates are self-assembled materials of purely inorganic origin, with an amorphous phase of silica intimately intertwined with a carbonate nanocrystalline phase. We propose a mechanism that explains all the morphologies described for biomorphs. Chemically coupled coprecipitation of carbonate and silica leads to fibrillation of the growing front and to laminar structures that experience curling at their growing rim. These curls propagate in a surflike way along the rim of the laminae. We show that all observed morphologies with smoothly varying positive or negative Gaussian curvatures can be explained by the combined growth of counterpropagating curls and growing laminae.

Minimal surface scaffold designs for tissue engineering

Triply-periodic minimal surfaces are shown to be a more versatile source of biomorphic scaffold designs than currently reported in the tissue engineering literature. A scaffold architecture with sheetlike morphology based on minimal surfaces is discussed, with significant structural and mechanical advantages over conventional designs. These sheet solids are porous solids obtained by inflation of cubic minimal surfaces to sheets of finite thickness, as opposed to the conventional network solids where the minimal surface forms the solid/void interface. Using a finite-element approach, the mechanical stiffness of sheet solids is shown to exceed that of conventional network solids for a wide range of volume fractions and material parameters. We further discuss structure-property relationships for mechanical properties useful for custom-designed fabrication by rapid prototyping. Transport properties of the scaffolds are analyzed using Lattice-Boltzmann computations of the fluid permeability. The large number of different minimal surfaces, each of which can be realized as sheet or network solids and at different volume fractions, provides design flexibility essential for the optimization of competing design targets.

The mechanisms of the formation and growth of water bubbles and associated dislocation loops in synthetic quartz

The development of water bubbles in synthetic quartz has been monitored by measurements of (i) the intensity of the light scattered and (ii) the increase in volume of the crystal, both as a function of temperature and time. These macroscopic measurements have been complemented by observations of the resulting microstructures, using transmission electron microscopy (TEM). A mechanism is proposed on the assumption that hydrogen is incorporated in the quartz structure by means of (4 H)Si defects. On heating, these defects diffuse and clusters develop. A cluster of n(4 H)Si produces a water bubble of (n−1)H2O, without any change of volume of the crystal. At any temperature T there is a critical bubble diameter above which the “steam” pressure P exceeds the pressure p for a spherical bubble in mechanical equilibrium. If P becomes greater than p, then the bubble increases in volume until P=p, the increase in volume being achieved by the pipe diffusion of Si and O away from the bubble site into a linked edge dislocation loop. This process produces the observed increase in volume of the crystal. The two diffusion processes take place virtually simultaneously and continue until all the (4 H)Si defects have been trapped in the bubbles. Values of the diffusion constant and the activation energy for the diffusion of the (4 H)Si defects are deduced. The relevance of these observations to the hydrolytic weakening of quartz is briefly discussed.

Bicontinuous structures in lyotropic liquid crystals and crystalline hyperbolic surfaces

Abstract The idealized structures of cubic bicontinuous mesophases in amphiphile—water systems are well described using minimal surfaces exhibiting cubic translational symmetry. The question of bicontinuity of noncubic mesophases, including some hexagonal and intermediate phases, remains open. Recent work has focused on the nature of phase transformations involving bicontinuous mesophases, leading to some understanding of the energetics that govern mesophase stability, and locations (if any) of neutral surfaces in swelling bilayers. Further advances await, regarding detailed probes of the topological ‘defect’ density in these systems, including channels and pores within the bilayer membrane. In addition to basic physical understanding of lyotropic mesomorphism, probes of topology are required to sort out differences between novel mesoporous solids, often templated using lyotropic liquid crystals. There is evidence for a bicontinuous morphology in ‘folded sheet materials’ derived from kanemite.

A Short History of an Elusive Yet Ubiquitous Structure in Chemistry, Materials and Mathematics

Herein we describe some properties and the occurrences of a beautiful geometric figure that is ubiquitous in chemistry and materials science, however, it is not as well-known as it should be. We call attention to the need for mathematicians to pay more attention to the richly structured natural world, and for materials scientists to learn a little more about mathematics. Our account is informal and eschews any pretence of mathematical rigor, but does start with some necessary mathematics. Regular figures such as the five regular Platonic polyhedra are an enduring part of human culture and have been known and celebrated for thousands of years. Herein we consider them as the five regular tilings on the surface of a sphere (a two-dimensional surface of positive curvature). A flag of a tiling of a two-dimensional surface consists of a combination of a coincident tile, edge, and vertex. A generally accepted definition of regularity is flag transitivity, which means that all flags are related by symmetries of the tiling (i.e. there is just one kind of flag). In addition to the five Platonic solids, there are three regular tilings of the plane (a surface of zero curvature), and these are the familiar coverings of the plane by triangles, squares, or hexagons tiled edge-to-edge. The corresponding regular tilings of three-dimensional space are also wellknown. Flags are now a polyhedron (tile) with a coincident face, edge, and vertex, and the regular tilings of the three-sphere are the six nonstellated regular polytopes of four dimensional space. We remark that four dimensions is the richest space in this regard; higher dimensions have only three regular polytopes (and of course three dimensions has five). However, in flat threedimensional (Euclidean) space, the space of our day-to-day experience, there is disappointingly only one regular tiling—the familiar space filling by cubes sharing faces (face-to-face). The classic reference to these figures is Coxeter!s Regular Polytopes, in which he remarks on the tilings of threedimensional Euclidean space: “For the development of a general theory, it is an unhappy accident that only one honeycomb [tiling] is regular...”. Unhappy indeed, because, perhaps as a consequence, the rich world of periodic graphs, which are the underlying topology of crystal structures, has been largely neglected by mathematicians. The graph associated with (carried by) the regular tiling by cubes is the set of edges and vertices. It is notably the structure of a form of elemental polonium, and chemists often refer to it as the a-Po net. Recently a system of symbols for nets has been developed and this net has the symbol pcu. Our review is concerned with another such periodic graph, and an associated surface.

Morphology: an ambiguous indicator of biogenicity.

This paper deals with the difficulty of decoding the origins of natural structures through the study of their morphological features. We focus on the case of primitive life detection, where it is clear that the principles of comparative anatomy cannot be applied. A range of inorganic processes are described that result in morphologies emulating biological shapes, with particular emphasis on geochemically plausible processes. In particular, the formation of inorganic biomorphs in alkaline silica-rich environments are described in detail.

Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples.

We present a method for geometric construction of periodic three-dimensional Euclidean nets by projecting two-dimensional hyperbolic tilings onto a family of triply periodic minimal surfaces (TPMSs). Our techniques extend the combinatorial tiling theory of Dress, Huson & Delgado-Friedrichs to enumerate simple reticulations of these TPMSs. We include a taxonomy of all networks arising from kaleidoscopic hyperbolic tilings with up to two distinct tile types (and their duals, with two distinct vertices), mapped to three related TPMSs, namely Schwarzs primitive (P) and diamond (D) surfaces, and Schoens gyroid (G).

Vertex symbols for zeolite nets

Symbols that specify the size and number of shortest rings at the angles of each of the 4-connected vertices of zeolite nets are given. Both the interpretation and the utility of these vertex symbols are discussed.

The chiral structure of porous chitin within the wing-scales of Callophrys rubi

The structure of the porous three-dimensional reticulated pattern in the wing scales of the butterfly Callophrys rubi (the Green Hairstreak) is explored in detail, via scanning and transmission electron microscopy. A full 3D tomographic reconstruction of a section of this material reveals that the predominantly chitin material is assembled in the wing scale to form a structure whose geometry bears a remarkable correspondence to the srs net, well-known in solid state chemistry and soft materials science. The porous solid is bounded to an excellent approximation by a parallel surface to the Gyroid, a three-periodic minimal surface with cubic crystallographic symmetry I4₁32, as foreshadowed by Stavenga and Michielson. The scale of the structure is commensurate with the wavelength of visible light, with an edge of the conventional cubic unit cell of the parallel-Gyroid of approximately 310 nm. The genesis of this structure is discussed, and we suggest it affords a remarkable example of templating of a chiral material via soft matter, analogous to the formation of mesoporous silica via surfactant assemblies in solution. In the butterfly, the templating is achieved by the lipid-protein membranes within the smooth endoplasmic reticulum (while it remains in the chrysalis), that likely form cubic membranes, folded according to the form of the Gyroid. The subsequent formation of the chiral hard chitin framework is suggested to be driven by the gradual polymerisation of the chitin precursors, whose inherent chiral assembly in solution (during growth) promotes the formation of a single enantiomer.