Universality of polyhedral linkages

The crystal structures of the long-known compound Na3(PO4)(H2O)6, tris-odium orthophosphate hexa-hydrate, and the compound Na3(PO4)(H2O)7, tris-odium orthophosphate hepta-hydrate, the possible existence of which is discussed in the literature, were elucidated by single-crystal X-ray diffraction. In both crystal structures, all the water mol-ecules are bound to the sodium cations, but the different water content leads to different arrangements in terms of polyhedral linkage. In the case of the hepta-hydrate (space group Pca21, Z = 4), this results in a layered structure made up from three sixfold coordinated Na+ cations with phosphate units in between. In the case of the hexa-hydrate (space group P1, Z = 4), a three-dimensional network is realised by one fivefold and five sixfold coordinated Na+ cations, in which the phosphate units are embedded in the voids. In both crystal structures, the water mol-ecules are involved in complex O-H⋯O hydrogen-bonding networks and form moderately strong hydrogen bonds on average, almost exclusively with the phosphate O atoms. It is noteworthy that some O atoms accept up to five such bonds.

Continuous Flattening and Reversing of Convex Polyhedral Linkages

Insights on the structure and properties of sodium iron phosphate glasses from molecular dynamics simulations

Abstract 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.

Structural features and rare earth ion clustering behavior in lanthanum phosphate and aluminophosphate glasses from molecular dynamics simulations

Abstract 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.

La2O3-Ga2O3 binary glass exhibits unusual optical properties owing to its high oxygen polarizability and low vibration energy. These optical properties include high refractive indices and a wide transmittance range. In this study, we performed classical molecular dynamics simulations on La2O3-Ga2O3 glass synthesized by an aerodynamic levitation technique. We have obtained structural models that reproduce experimental results, such as NMR, high-energy X-ray diffraction, and neutron diffraction. Based on our analysis, the structural features were clarified: 5-, 6-coordinated Ga, edge-sharing GaOx-GaOx polyhedral linkages, and oxygen triclusters. Additionally, the vibrational density of states was calculated by diagonalization of the dynamical matrix derived from the structural models and the results were compared with Raman scattering spectra. The mode analysis of the Raman spectra revealed that the principal bands at 650 cm-1 were mainly attributed to the stretching modes of the bridging and nonbridging oxygens. Meanwhile, the shoulder bands at the highest frequency of 750 cm-1 were mainly attributed to the stretching modes of the bridging oxygens and oxygen triclusters. The structural models obtained in this study well describe the characteristic local structures and vibrational properties of the La2O3-Ga2O3 glass.

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.

Effect of ZrO2 on the structure and properties of soda-lime silicate glasses from molecular dynamics simulations

We report the crystal structure of a dehydration product of the mineral kaňkite (FeAsO 4 · 3.5H 2 O). The structure was solved and refined by precession electron diffraction tomography. Initially, we believed that we solved the structure of kaňkite; this mineral, however, decomposes in vacuum to Fe 2 (AsO 4 )(HAsO 4 )(OH)(H 2 O) 3 (=FeAsO 4 · 2H 2 O). The crystal structure was solved in the space group Cc and the model was refined by the full-matrix least-squares method by Jana2006. The model converged to R (obs) = 12.02 %, wR (obs) = 12.49 % (with GOF = 6.39) for 1139 observed reflections with [ I obs > 3σ( I )]. The structure of the dehydration product of kaňkite consists of corrugated heteropolyhedral sheets. Pairs of Feϕ 6 octahedra, flanked by five adjacent arsenate tetrahedra, could be seen as the building units of the corrugated sheets. Variable-temperature powder X-ray diffraction showed that kaňkite dehydrates to FeAsO 4 · 2H 2 O at 55–56°C. Based on the similar topology of FeAsO 4 · 2H 2 O and the mineral lausenite [Fe 2 (SO 4 ) 3 · 5H 2 O], and the structural relationship between lausenite and kornelite [Fe 2 (SO 4 ) 3 · 7.5H 2 O], we conjecture that the structure of kaňkite could be also built by corrugated sheets. One polyhedral linkage between an Feϕ 6 octahedron and an Asϕ 4 tetrahedron in the sheet of the dehydrated kaňkite needs to be broken to allow for stretching of the sheets, the introduction of an additional H 2 O molecule into the sheet and perhaps also additional H 2 O molecules in between the sheets.

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.

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

Zr environment and nucleation role in aluminosilicate glasses

Structure of Fe(III) precipitates generated by the electrolytic dissolution of Fe(0) in the presence of groundwater ions

Design and kinematic analysis of a novel prism deployable mechanism

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.

Homothetic Jitterbug-like linkages

Design and Analysis of Mast Based on Spatial Polyhedral Linkages Mechanism along Radial Axes

Single crystals of α-Ba2P2O7, dibarium diphosphate, were obtained by solid-state reaction. The ortho­rhom­bic structure is isotypic with α-Sr2P2O7 and is the second polymorph obtained for this composition. The structure is built from two different BaO9 polyhedra (both with m symmetry), with Ba—O distances in the ranges 2.7585 (10)–3.0850 (6) and 2.5794 (13)–2.9313 (4) Å. These polyhedra are further linked by sharing corners along [010] and either edges or triangular faces perpendicularly to [010] to form the three-dimensional framework. This polyhedral linkage delimits large channels parallel to [010] where the P2O7 diphosphate anions are located. These groups (symmetry m) are characterized by a P—O—P angle of 131.52 (9)° and an eclipsed conformation. They are connected to the BaO9 polyhedra through edges and corners.