Universality of polyhedral linkages

In this paper new overconstrained mechanisms are described which are synthesized by inserting equal basic mechanisms known as Nuremberg scissors into the edges of a Platonian polyhedron and interconnecting them at their ends by different kinds of articulations. The basic mechanism is a planar mechanism and can be inserted into an edge of a Platonian polyhedron in two different ways: either its plane becomes identical with the plane given by the edge line and the center of the polyhedron or orthogonal to this plane. For each of these two insertions two different kinds of articulation (located at the apexes of the polyhedron) are proposed in the paper. Four different kinds of new polyhedral linkages are thus obtained whose syntheses are decribed in detail. A corkscrew on the market under the commercial name Zig-Zag is based on Nuremberg scissors. As the common parts in the newly designed linkages are Nuremberg scissors we adopt this name for the whole family of new polyhedral linkages which are, though highly overconstrained, movable with one degree of freedom.

Design and kinematic analysis of a novel prism deployable mechanism

Goethite (α-FeOOH) is abundant at the Earth’s surface and has the unusual capacity to adsorb and fix ions from migrating solutions. Understanding the mechanisms by which foreign elements are incorporated into natural goethite has implications for environmental and mining problems. X-ray absorption spectroscopy (XAS) was used to obtain structural information on the local environment around Ni in natural Ni-containing goethite (1.8-4.1 mol% Ni) from Vermelho lateritic deposit of Serra dos Carajás (Brazil) and in synthetic analogues. The data were collected at the LNLS XAS beam line at the Ni and Fe K-edges, at room temperature, and at the Ni K-edge at 8 K. Nickel was found in essentially the same environment in all natural and synthetic samples, with negligible thermal disorder. The coordination polyhedron is a tetragonal dipyramid of oxygen atoms showing that Ni preserves its usual local symmetry. This finding is compatible with a model in which substitution of Ni for Fe is accompanied by a proton capture resulting in NiO2(OH)4 octahedra. The polyhedral linkages are similar to that of pure a-FeOOH, consisting of four shared edges at about the same metal-metal distances, as in the pure mineral. The third and longest metal-metal distance is about 6% larger than the expected corner-sharing distance in the α-FeOOH structure, showing that incorporation of Ni locally distorts and opens the structure.

Raman spectroscopy and the powder diffraction technique have been used to monitor the recovery process of two partially metamict zircons (2.6 and 4.8 × 1018α-decays g−1) from Sri Lanka during a series of isothermal annealing experiments in the temperature range from 870 to 1622 K. These experiments show for the first time that structural recovery in partially metamict zircon proceeds via three distinct recovery stages, each of which occurs within a distinct time-temperature regime. Whereas the first two stages have previously been recognized (recovery of damaged crystalline remnants and epitaxial recrystallization), the third stage has not yet been identified as a single activated process. It is suggested that anisotropic defect annealing during the first stage at low temperatures, where the structure recovers preferentially along the a(b) plane, produces a geometrical situation where large structural rearrangements are necessary to remove the remaining defects inside the crystalline material. This situation is approximately reached when the amorphous domains start to recrystallize. The reason for anisotropic annealing can be found in a different connectivity between polyhedral linkages in both directions of the zircon lattice. High apparent activation energies, in the range of 6.4 to 7.9 eV, were determined for the third recovery stage from the Raman data, which are interpreted to reflect large structural rearrangements (i.e. polyhedral tilting) associated with the final recovery of the c axis. This explains the occurrence of a distinct recrystallization stage without defect annealing. Finally, it should be mentioned that the first recovery stage is not necessarily expected to occur in less damaged zircon crystals (<∼2 × 1018α-decays g−1), since less stable defects along the basal plane might have already been self-annealed during radiation damage accumulation under ambient temperatures.

Novel phosphate halides BaMnIII[PO4]FCl and BaMnIII[PO4]F2: Effects of mixed halides on crystal structures and magnetic properties

The Fulleroid, discovered by K. Wohlhart, is a 48-link overconstrained spatial linkage which expands and contracts within a rhombic dodecahedral boundary. In this paper, some similar types of linkages are synthesized based on some observations on the Fulleroid. First an infinite class of 24-faced polyhedral linkages is described. Next the idea is generalized for polyhedra having rhombic faces. Then analyzing these linkages a basic closed chain is derived as a module and some dipyramidal and stellated polyhedral linkages are synthesized using this module.

We study a discrete attachment model for the self-assembly of polyhedra called the building game. We investigate two distinct aspects of the model: (i) enumerative combinatorics of the intermediate states and (ii) a notion of Brownian motion for the polyhedral linkage defined by each intermediate that we term conformational diffusion. The combinatorial configuration space of the model is computed for the Platonic, Archimedean, and Catalan solids of up to 30 faces, and several novel enumerative results are generated. These represent the most exhaustive computations of this nature to date. We further extend the building game to include geometric information. The combinatorial structure of each intermediate yields a systems of constraints specifying a polyhedral linkage and its moduli space. We use a random walk to simulate a reflected Brownian motion in each moduli space. Empirical statistics of the random walk may be used to define the rates of transition for a Markov process modeling the process of self-assembly.

Polyhedral Linkages

In this study, assemblies of Bennett loops constructing regular polygonal linkages and regular polyhedral linkages are presented. The regular polyhedral linkages, necessarily, depend on spherical polyhedral shapes. Most of the resulting linkages have single degree of freedom, but there are exceptions such as a cubic linkage.

The study aims to devise means of obtaining polyhedral linkages for homothetic deployment of polyhedral shapes by embedding planar link groups in faces of the polyhedral shape of interest. The questions of which polyhedral shapes may be suitable for such a purpose and what are the compatibility conditions for spatially assembling planar link groups are addressed. Homohedral and tangential polyhedral shapes are found to be suitable for the task and some examples of linkages are worked out.

Predicting the chemical durability of glass materials is important for various applications from daily life such as cell phone screens and kitchenware to advanced technologies such as nuclear waste disposal and biomedicine. In this work, we explored the prediction of the initial glass dissolution rates using structural features from molecular dynamics (MD) simulations for a series of glass compositions (total 28), including ZrO2‐ and V2O5‐containing boroaluminosilicate, borosilicate, and aluminosilicate glasses. The initial dissolution rates (r0) measured experimentally at 90°C with varying solution conditions were correlated with structural features (e.g., polyhedral linkages and non‐bridging oxygen species) obtained from MD simulations, either from this study or from literature. As hydrolysis of the glass network through breaking of the network former linkages (e.g., Si–O–Si, Si–O–Al, etc.) is a critical step of network glass dissolution, the statistics of these linkages obtained from MD were also correlated to r0 through linear regression, where the coefficients of determination (R2) and root mean square error are found to be 0.949 and 0.681, respectively. This model was compared and discussed with existing models developed by various approaches, including machine learning, the kinetic rate equation, topological constraint theory, and other descriptors from MD simulations. The discussion provides insights on future model improvements to predict glass dissolution. In addition, as the effect of V2O5 on glass dissolution was not well studied comparing to ZrO2, the impact of V2O5 was emphasized in this paper, suggesting that the impact is not the same across all glass compositions and test conditions.

In this paper we present a new type of over-constrained spatial linkages obtained by inserting planar double-ring mechanisms (modules) into the faces of a polyhedron so that they form closed networks over the polyhedron after being interconnected by appropriate gussets. Such linkages will be called “double-ring polyhedral linkages”. Though highly over constrained, these linkages are deformable with one degree of freedom. Recently it was shown that polyhedral linkages can be synthesized with single ring mechanisms as modules. Therefore the question arises: what is the advantage of using double-ring mechanisms as modules instead of single-ring mechanisms? The first answer is: double-ring polyhedral linkages show much greater global stability. This is proved by all manufactured models, and the reason is evident: the single-ring mechanism has twice as many degrees of freedom as there are sides in the polyhedral face into which it is inserted, while the double-ring mechanism is movable with only one degree of freedom. A second answer is: from a double-ring polyhedral linkages a variety of cup-like linkages can be found by simply dividing them into parts.

Crystal structure of Fe2(AsO4)(HAsO4)(OH)(H2O)3, a dehydration product of kaňkite

High‐alumina containing high‐level waste (HLW) will be vitrified at the Waste Treatment Plant at the Hanford Site. The resulting glasses, high in alumina, will have distinct composition‐structure‐property (C‐S‐P) relationships compared to previously studied HLW glasses. These C‐S‐P relationships determine the processability and product durability of glasses and therefore must be understood. The main purpose of this study is to understand the detailed structural changes caused by Al:Si and (Al + Na):Si substitutions in a simplified nuclear waste model glass (ISG, international simple glass) by combining experimental structural characterizations and molecular dynamics (MD) simulations. The structures of these two series of glasses were characterized by neutron total scattering and 27 Al, 23 Na, 29 Si, and 11 B solid‐state nuclear magnetic resonance (NMR) spectroscopy. Additionally, MD simulations were used to generate atomistic structural models of the borosilicate glasses and simulation results were validated by the experimental structural data. Short‐range (eg, bond distance, coordination number, etc) and medium‐range (eg, oxygen speciation, network connectivity, polyhedral linkages) structural features of the borosilicate glasses were systematically investigated as a function of the degree of substitution. The results show that bond distance and coordination number of the cation‐oxygen pairs are relatively insensitive to Al:Si and (Al + Na):Si substitutions with the exception of the B‐O pair. Additionally, the Al:Si substitution results in an increase in tri‐bridging oxygen species, whereas (Al + Na):Si substitution creates nonbridging oxygen species. Charge compensator preferences were found for Si‐[NBO] (Na + ), [3] B‐[NBO] (Na + ), [4] B (mostly Ca 2+ ), [4] Al (nearly equally split Na + and Ca 2+ ), and [6] Zr (mostly Ca 2+ ). The network former‐BO‐network former linkages preferences were also tabulated; Si‐O‐Al and Al‐O‐Al were preferred at the expense of lower Si‐O‐ [3] B and [3] B‐O‐ [3] B linkages. These results provide insights on the structural origins of property changes such as glass‐transition temperature caused by the substitutions, providing a basis for future improvements of theoretical and computer simulation models.

The aim of this study is to present a novel shape-transformable polyhedral mechanism namely, the TrT–T mechanism, which can transform between a truncated tetrahedron and a common tetrahedron. The conceptual model of the TrT–T mechanism is proposed and described. For one-degree-of-freedom objective, a hexagonal planar linkage is chosen as a hexagonal interlinked unit to develop a solid model and fabricate a prototype. Mobility analysis is carried out based on screw theory. The inverse and forward kinematics are investigated, and the singularity is analyzed. The trajectories and velocities of the hinge points are described and explored. The prototype and simulation results demonstrate the feasibility of the TrT–T mechanism for shape transformation and validate the correctness of the mobility analysis. As a novel polyhedral linkage, the TrT–T mechanism can be potentially applied to modules with shape-transformation ability for constructing reconfigurable and modular robots.