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At least 145 records · Page 8

One Electron Multiple Proton Transfer in Model Organic Donor–Acceptor Systems: Implications for High-Frequency EPR

EPR spectroscopy is an important spectroscopic method for identification and characterization of radical species involved in many biological reactions. The tyrosyl radical is one of the most studied amino acid radical intermediates in biology. Often in conjunction with histidine residues, it is involved in many fundamental biological electron and proton transfer processes, such as in the water oxidation in photosystem II. As biological processes are typically extremely complicated and hard to control, molecular bio-mimetic model complexes are often used to clarify the mechanisms of the biological reactions. In this work, we present theoretical calculations to investigate the sensitivity of magnetic resonance parameters to proton-coupled electron transfer events, as well as conformational substates of the molecular constructs which mimic the tyrosine-histidine (Tyr-His) pairs found in a large variety of proteins. Upon oxidation of the phenol, the Tyr analog, these complexes can perform not only one-electron one-proton transfer (EPT), but also one-electron two-proton transfers (E2PT). It is shown that in aprotic environment the g X -components of the electronicg-tensor are extremely sensitive to the first proton transfer from the phenoxyl oxygen to the imidazole nitrogen (EPT product), leading to a significant increase of the g X -value of up to 0.003, but are not sensitive to the second proton transfer (E2PT). In the latter case, the change of the g X -value is much smaller (ca. 0.0001), which is too small to be distinguished even by high-frequency EPR. The 14 N hyperfine values are also too similar to allow differentiation between the different protonation states in EPT and E2PT. The magnetic resonance parameters were also calculated as a function of the rotation angles around single bonds. It was demonstrated that rotation of the phenoxyl group results in large positive changes (> 0.001) in the g X -values. Analysis of the data reveals that the main source of these changes is related to the strength of the H-bond between phenoxyl oxygen and the proton(s) on N 1 and N 2 positions of the imidazole.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Elucidating the temperature and density dependence of silver chloride hydration numbers in high-temperature water vapor: A first-principles molecular simulation study

Hydration numbers of metal complexes in low-density aqueous solutions are required for developing geochemical models for ore-forming metals and for designing supercritical desalination processes. In this study, we investigate the temperature and density dependence of the hydration numbers of silver chloride at 623 K, 673 K, and 713 K and densities of 10–100 kg/m 3 . Experimental estimates of the hydration number in the literature for AgCl at these conditions are inconclusive and possibly contradictory as to the temperature and density dependence. First-principles molecular simulation presents an attractive alternative to experimental measurements. Specifically, recent work shows that machine-learning-accelerated nested Monte Carlo simulations provide reliable estimates for the hydration numbers of CuCl at 623 K from 10 to 100 kg/m 3 . Using the same technique, we find a monotonic temperature dependence, with the hydration number decreasing slightly with increasing temperature. In addition, the simulation-predicted hydration numbers steadily increase with increasing density. These temperature and density trends are in agreement with certain experimental data sets. Therefore, this work demonstrates how first-principles Monte Carlo simulations assist in resolving discrepancies between experimental data sets. Our simulation results also correctly predict that the hydration number, and thus also the solubility, of AgCl is lower than that of CuCl under the same conditions. Furthermore, the bond length and angle formed between the water complex and AgCl differ from those for CuCl, consistent with the lower solubility of AgCl.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Physical structure of constitutional isomers influences antiproliferation activity of thiosemicarbazone-alkylthiocarbamate copper complexes

A series of hybrid thiosemicarbazone-alkylthiocarbamate copper complexes with similar electronic environments but distinct physical structures have been prepared, characterized, and evaluated for antiproliferation activity. The complexes include the constitutional isomers (1-phenylpropane-1-imine-(O-ethylthiocarbamato)-2-one-(N-methylthiosemicarbazonato))copper(II) (CuL 1 ) and (1-phenylpropane-1-one-(N-methylthiosemicarbazonato)-2-imine-(O-ethylthiocarbamato))copper(II) (CuL 2 ) along with (1-propane-1-imine-(O-ethylthiocarbamato)-2-one-(N-methylthiosemicarbazonato))copper(II) (CuL 3 ). Complexes CuL 1 and CuL 2 differ in the positions of the pendent thiosemicarbazone (TSC) and alkylthiocarbamate (ATC) moieties on the 1-phenylpropane backbone. Complex CuL 3 employs a propane backbone with the TSC in the 2-position as in CuL 1 . The isomer pair CuL 1 and CuL 2 have equivalent electronic environments with indistinguishable Cu II/I potentials (E 1/2 = -0.86 V vs. ferrocenium/ferrocene) and electron paramagnetic resonance (EPR) spectra (g ∥ = 2.26, g ⊥ = 2.08). The electronic structure of CuL 3 has a similar E 1/2 of -0.84 V and identical EPR parameters to CuL 1, 2 . Single crystal X-ray diffraction studies confirm a consistent donor environment with no substantial variation in the Cusingle bondN or Cusingle bondS bond distances and angles between the complexes. The antiproliferation activities of the CuL 1–3 were evaluated against the lung adenocarcinoma cell line (A549) and nonmalignant lung fibroblast cell line (IMR-90) using the MTT assay. CuL 1 had the highest A549 activity ( A549 EC 50 = 0.065 μM) and selectivity ( IMR-90 EC 50 / A549 EC 50 = 20). The constitutional isomer CuL 2 displayed decreased A549 activity (0.18 μM) and selectivity (10.6). The complex CuL 3 displayed activity (0.009 μM) similar to CuL 1 but with a lack of selectivity (1.0). Cellular copper loading determined by ICP-MS was consistent with the activity and selectivity trends. The complexes CuL 1–3 did not induce reactive oxygen species (ROS) generation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effect of layer bending on montmorillonite hydration and structure from molecular simulation

Conceptual models of smectite hydration include planar (flat) clay layers that undergo stepwise expansion as successive monolayers of water molecules fill the interlayer regions. However, X-ray diffraction (XRD) studies indicate the presence of interstratified hydration states, suggesting non-uniform interlayer hydration in smectites. Additionally, recent theoretical studies have shown that clay layers can adopt bent configurations over nanometer-scale lateral dimensions with minimal effect on mechanical properties. Therefore, in this study we used molecular simulations to evaluate structural properties and water adsorption isotherms for montmorillonite models composed of bent clay layers in mixed hydration states. Results are compared with models consisting of planar clay layers with interstratified hydration states (e.g. 1W–2W). The small degree of bending in these models (up to 1.5 Å of vertical displacement over a 1.3 nm lateral dimension) had little or no effect on bond lengths and angle distributions within the clay layers. Except for models that included dry states, porosities and simulated water adsorption isotherms were nearly identical for bent or flat clay layers with the same averaged layer spacing. Similar agreement was seen with Na- and Ca-exchanged clays. In conclusion, while the small bent models did not retain their configurations during unconstrained molecular dynamics simulation with flexible clay layers, we show that bent structures are stable at much larger length scales by simulating a 41.6×7.1 nm 2 system that included dehydrated and hydrated regions in the same interlayer.

58 GEOSCIENCES↗

MD Simulation of Water Using a Rigid Body Description Requires a Small Time Step to Ensure Equipartition

In simulations of aqueous systems, it is common to freeze the bond vibration and angle bending modes in water to allow for a longer time step δt for integrating the equations of motion. Thus, δt = 2 fs is often used in simulating rigid models of water. We simulate the SPC/E model of water using δt from 0.5 to 3.0 fs and up to 4 fs using hydrogen mass repartitioning. In these simulations, we find that for all but δt = 0.5 fs, equipartition is not obtained between translational and rotational modes, with the rotational modes exhibiting a lower temperature than the translation modes. To probe the reasons for the lack of equipartition, we study the autocorrelation of the translational velocity of the center of mass and the angular velocity of the rigid water molecule, respectively. Here, we find that the rotational relaxation occurs on a timescale comparable to vibrational periods, calling into question the original motivations for freezing the vibrations. Furthermore, a time step with δt ≥ 1 fs is not able to capture accurately the fast rotational relaxation, which reveals its impact as an effective slowing-down of rotational relaxation. The fluctuation–dissipation relation then leads to the conclusion that the rotational temperature should be cooler for δt greater than the reference value of 0.5 fs. Consideration of fluctuation–dissipation in equilibrium molecular dynamics simulations also emphasizes the need to capture the temporal evolution of fluctuations with fidelity and the role of δt in this regard. The time step also influences the solution thermodynamic properties: both the mean system potential energies and the excess entropy of hydration of a soft repulsive cavity are sensitive to δt.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Molecular structure retrieval directly from laboratory-frame photoelectron spectra in laser-induced electron diffraction

Ubiquitous to most molecular scattering methods is the challenge to retrieve bond distance and angle from the scattering signals since this requires convergence of pattern matching algorithms or fitting methods. This problem is typically exacerbated when imaging larger molecules or for dynamic systems with little a priori knowledge. Here, we employ laser-induced electron diffraction (LIED) which is a powerful means to determine the precise atomic configuration of an isolated gas-phase molecule with picometre spatial and attosecond temporal precision. We introduce a simple molecular retrieval method, which is based only on the identification of critical points in the oscillating molecular interference scattering signal that is extracted directly from the laboratory-frame photoelectron spectrum. The method is compared with a Fourier-based retrieval method, and we show that both methods correctly retrieve the asymmetrically stretched and bent field-dressed configuration of the asymmetric top molecule carbonyl sulfide (OCS), which is confirmed by our quantum-classical calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Local lattice distortions and electronic phases in perovskite manganite Pr 0.5 Sr 0.5 MnO 3

We use variable temperature and magnetic field total x-ray scattering to study the crystal structure of the strongly correlated Pr 0.5 Sr 0.5 MnO 3 perovskite, which is a paramagnetic insulator at room temperature, becomes a ferromagnetic metal at 272 K and, upon further decreasing the temperature, turns into an antiferromagnetic insulator at 105 K. We find that a model featuring a monoclinic symmetry captures the structure and its temperature and field evolution well, eliminating the need to evoke a phase segregation scenario as done in prior studies. It appears that coupled variations in Mn–oxygen bonding distances and angles from their values in an undistorted perovskite lattice, i.e., coupled local lattice distortions, assist the phase transitions in Pr 0.5 Sr 0.5 MnO 3 , contributing to its unique physical properties. Local structural distortions thus emerge as an important degree of freedom in strongly correlated systems, in particular perovskite manganates, and, therefore, they should be fully accounted for when their fascinating physics is considered.

36 MATERIALS SCIENCE↗

Multilevel atomic structural model for interstratified opal materials

The structure of opal has long fascinated scientists. It occurs in a number of structural states, ranging from amorphous to exhibiting features of stacking disorder. Opal-CT, where C and T signify cristobalite- and tridymite-like interstratification, represents an important link in the length scales between amorphous and crystalline states. However, details about local atomic (dis)order and arrangements extending to long-range stacking faults in opal polymorphs remain incompletely understood. Here, a multilevel modeling approach is reported that considers stacking states in correlation with the abundance of C and T segments as a high-level structural parameter (i.e. not each atom). Optimization accounting for inter-tetrahedral bond lengths and angles and the regularity of the silicate tetrahedra is included as lower levels of structural parameters. Together, a set of parameters with both coarse-grained and atomistic features for different levels of structural details is refined. Structural disorder at the ~10–100 Å distance scale is evaluated using experimental pair distribution function and diffraction datasets, comparing peak intensities, widths and asymmetry. Here this work presents a complete multilevel structural description of natural opal-CT and explains many of the unusual features observed in X-ray powder diffraction patterns. This modeling approach can be adopted generally for analyzing layered materials and their assembly into 3D structures.

36 MATERIALS SCIENCE↗

Arginine off-kilter: guanidinium is not as planar as restraints denote

Crystallographic refinement of macromolecular structures relies on stereochemical restraints to mitigate the typically poor data-to-parameter ratio. For proteins, each amino acid has a unique set of geometry restraints which represent stereochemical information such as bond lengths, valence angles, torsion angles, dihedrals and planes. It has been shown that the geometry in refined structures can differ significantly from that present in libraries; for example, it was recently reported that the guanidinium moiety in arginine is not symmetric. In this work, the asymmetry of the N ∊ —C ζ —N η1 and N ∊ —C ζ —N η2 valence angles in the guanidinium moiety is confirmed. In addition, it was found that the C δ atom can deviate significantly (more than 20°) from the guanidinium plane. This requires the relaxation of the planar restraint for the C δ atom, as it otherwise causes the other atoms in the group to compensate by distorting the guanidinium core plane. A new set of restraints for the arginine side chain have therefore been formulated, and are available in the software package Phenix , that take into account the asymmetry of the group and the planar deviation of the C δ atom. This is an example of the need to regularly revisit the geometric restraint libraries used in macromolecular refinement so that they reflect the best knowledge of the structural chemistry of their components available at the time.

59 BASIC BIOLOGICAL SCIENCES↗

Analysis of Bis(trifluoromethylsulfonyl)imide Interactions with Metal Cations Through a Chemical Informatics Approach

Nominally weakly coordinating anions are useful for modulating the solubility and chemical properties of metal complexes, but identification and analysis of the systematics of the interactions of anions with cationic metal complexes has not received the attention it deserves. Here, a chemical informatics approach is demonstrated for identifying and quantitatively analyzing the ways that the bis(trifluoromethylsulfonyl)imide anion (TFSI) can interact with metal-containing species. An open access computer program (PyCIFTer) was developed to facilitate large-scale structural analysis of TFSI-containing species by utilization of experimental atomic coordinate data from single-crystal X-ray diffraction (XRD) studies obtained from the Cambridge Structural Database (CSD). PyCIFTer establishes a three-dimensional vector space from the raw atomic coordinates, generating acyclic, undirected graphs that are used to rapidly analyze the structural properties (bond lengths and angles) of TFSI in individual structures in sequential/batch fashion. The structures are sorted by PyCIFTer into groups based on pre-set and chemically sensible criteria, affording a comprehensive and systematic view of TFSI structural chemistry. This approach avoids tedious one-at-a-time interrogation of structures, a prospect unreasonable in this case, and many others of contemporary chemical relevance; there were over 1500 structures in the CSD containing TFSI as of November 2024. The results demonstrate that TFSI only rarely binds to cations in the solid state, favoring the formation of species in which TFSI is found in cations’ outer coordination spheres. The prospect of applying PyCIFTer to other moieties is also discussed. PyCIFTer is also schematically compared to the commercial CSD Python application programming interface (API). Taken together, this work demonstrates the usefulness of modular workflows for sequential/batch analysis of structural data from XRD, an approach that appears poised to accelerate the translation of legacy structural results into new chemical insights and hypotheses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Non-classical adhesive-bonded joints in practical aerospace construction

Solutions are derived for adhesive-bonded joints of non-classical geometries. Particular attention is given to bonded doublers and to selective reinforcement by unidirectional composites. Non-dimensionalized charts are presented for the efficiency limit imposed on the skin as the result of the eccentricity in the load path through the doubler. It is desirable to employ a relativly large doubler to minimize the effective eccentricity in the load path. The transfer stresses associated with selective reinforcement of metal structures by advanced composites are analyzed. Reinforcement of bolt holes in composites by bonded metal doublers is covered quantitatively. Also included is the adhesive joint analysis for shear flow in a multi-cell torque box, in which the bond on one angle becomes more critical sooner than those on the others, thereby restricting the strength to less than the total of each maximum strength when acting alone. Adhesive plasticity and adherend stiffness and thermal imbalances are included. A simple analysis/design technique of solution in terms of upper and lower bounds on an all-plastic adhesive analysis is introduced.

Hart-Smith, L. J.↗

Fiber reinforced solids possessing great fracture toughness: The role of interfacial strength

The results of angle-ply investigations for strength and toughness of brittle fiber/brittle filament composites are presented. General results are discussed for both unidirectional and angle-ply intermittently bonded boron/epoxy composites as affected by soaking and freezing water environments. A description of and the operating instructions are included for the modified 230 mm (9 inch) wide intermittent coating tape making apparatus.

Atkins, A. G.↗

Theory of metal atom-water interactions and alkali halide dimers

Theoretical studies of the interactions of metal atoms with water and some of its isoelectronic analogs, and of the properties of alkali halides and their aggregates are discussed. Results are presented of ab initio calculations of the heats of reaction of the metal-water adducts and hydroxyhydrides of Li, Be, B, Na, Mg, and Al, and of the bond lengths and angles an; the heats of reaction for the insertion of Al into HF, H2O, NH3, H2S and CH3OH, and Be and Mg into H2O. Calculations of the electron affinities and dipole moments and polarizabilities of selected gas phase alkali halide monomers and dimers are discussed, with particular attention given to results of calculations of the polarizability of LiF taking into account electron correlation effects, and the polarizability of the dimer (LiF)2.

Jordan, K. D.↗

Molecular arrangements and conformations of liquid n-tridecane chains confined between two hard walls

Monte Carlo simulations based on united CH2 atoms linked with fixed bond lengths and angles, and continuously varying torsional angles subject to appropriate interaction energies, were used to study liquid n-tridecane chains confined between two parallel hard walls with 5 mm separation. The molecules located in the central region are noted to be in very close agreement with ideal unperturbed chains. Nearly all the chain units in the first segmental layer adjacent to the walls belong to two-dimensional chains, and exhibit considerable orientational correlations between neighboring segments of different chains.

Vacatello, Michele↗

Voyager disk-integrated photometry of Triton

Hapke's (1981) photometric model has been combined with a plane-parallel thin atmospheric haze model to describe Voyager whole-disk observations of Triton, in the violet, blue, and green wavelength bands, in order to obtain estimates of Triton's geometric albedo, phase integral, and Bond albedo. Phase angle coverage in these filters ranging from about 12 to 159 deg was obtained by combining narrow- and wide-angle camera images. An upturn in the data at the highest phase angles observed can be explained by including scattering in a thin atmospheric haze layer with optical depths systematically decreasing with wavelength from about 0.06 in the violet to 0.03 for the green filter data.

Hillier, J.↗

Internal vibrations of a molecule consisting of rigid segments. I - Non-interacting internal vibrations

For molecular crystals, a procedure is proposed for interpreting experimentally determined atomic mean square anisotropic displacement parameters (ADPs) in terms of the overall molecular vibration together with internal vibrations with the assumption that the molecule consists of a set of linked rigid segments. The internal librations (molecular torsional or bending modes) are described using the variable internal coordinates of the segmented body. With this procedure, the experimental ADPs obtained from crystal structure determinations involving six small molecules (sym-trinitrobenzene, adenosine, tetra-cyanoquinodimethane, benzamide, alpha-cyanoacetic acid hydrazide and N-acetyl-L-tryptophan methylamide) have been analyzed. As a consequence, vibrational corrections to the bond lengths and angles of the molecule are calculated as well as the frequencies and force constants for each internal torsional or bending vibration.

He, X. M.↗

Materials Data on Mn9Al8Fe3(SiO4)12 by Materials Project

Mn9Fe3Al8(SiO4)12 crystallizes in the monoclinic C2 space group. The structure is three-dimensional. there are six inequivalent Mn2+ sites. In the first Mn2+ site, Mn2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Mn–O bond distances ranging from 2.27–2.44 Å. In the second Mn2+ site, Mn2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Mn–O bond distances ranging from 2.27–2.44 Å. In the third Mn2+ site, Mn2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Mn–O bond distances ranging from 2.27–2.44 Å. In the fourth Mn2+ site, Mn2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are a spread of Mn–O bond distances ranging from 2.27–2.44 Å. In the fifth Mn2+ site, Mn2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.27 Å) and four longer (2.43 Å) Mn–O bond lengths. In the sixth Mn2+ site, Mn2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.27 Å) and four longer (2.43 Å) Mn–O bond lengths. There are two inequivalent Fe2+ sites. In the first Fe2+ site, Fe2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.25 Å) and four longer (2.42 Å) Fe–O bond lengths. In the second Fe2+ site, Fe2+ is bonded in a distorted body-centered cubic geometry to eight O2- atoms. There are four shorter (2.25 Å) and four longer (2.42 Å) Fe–O bond lengths. There are four inequivalent Al3+ sites. In the first Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share corners with six SiO4 tetrahedra. There is four shorter (1.91 Å) and two longer (1.92 Å) Al–O bond length. In the second Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share corners with six SiO4 tetrahedra. There is three shorter (1.91 Å) and three longer (1.92 Å) Al–O bond length. In the third Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share corners with six SiO4 tetrahedra. There is three shorter (1.91 Å) and three longer (1.92 Å) Al–O bond length. In the fourth Al3+ site, Al3+ is bonded to six O2- atoms to form AlO6 octahedra that share corners with six SiO4 tetrahedra. There is four shorter (1.91 Å) and two longer (1.92 Å) Al–O bond length. There are eight inequivalent Si4+ sites. In the first Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with four AlO6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Si–O bond lengths are 1.66 Å. In the second Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with four AlO6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Si–O bond lengths are 1.66 Å. In the third Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with four AlO6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Si–O bond lengths are 1.66 Å. In the fourth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with four AlO6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Si–O bond lengths are 1.66 Å. In the fifth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with four AlO6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Si–O bond lengths are 1.66 Å. In the sixth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with four AlO6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Si–O bond lengths are 1.66 Å. In the seventh Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with four AlO6 octahedra. The corner-sharing octahedra tilt angles range from 47–48°. All Si–O bond lengths are 1.66 Å. In the eighth Si4+ site, Si4+ is bonded to four O2- atoms to form SiO4 tetrahedra that share corners with four AlO6 octahedra. The corner-sharing octahedral tilt angles are 47°. All Si–O bond lengths are 1.66 Å. There are twenty-four inequivalent O2- sites. In the first O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the second O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the third O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the fourth O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the fifth O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the sixth O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the seventh O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, one Fe2+, one Al3+, and one Si4+ atom. In the eighth O2- site, O2- is bonded in a 4-coordinate geometry to two Fe2+, one Al3+, and one Si4+ atom. In the ninth O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the tenth O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, one Fe2+, one Al3+, and one Si4+ atom. In the eleventh O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, one Fe2+, one Al3+, and one Si4+ atom. In the twelfth O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, one Fe2+, one Al3+, and one Si4+ atom. In the thirteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, one Fe2+, one Al3+, and one Si4+ atom. In the fourteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, one Fe2+, one Al3+, and one Si4+ atom. In the fifteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the sixteenth O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, one Fe2+, one Al3+, and one Si4+ atom. In the seventeenth O2- site, O2- is bonded in a 4-coordinate geometry to one Mn2+, one Fe2+, one Al3+, and one Si4+ atom. In the eighteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Fe2+, one Al3+, and one Si4+ atom. In the nineteenth O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the twentieth O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the twenty-first O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the twenty-second O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the twenty-third O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom. In the twenty-fourth O2- site, O2- is bonded in a 4-coordinate geometry to two Mn2+, one Al3+, and one Si4+ atom.

36 MATERIALS SCIENCE↗

Critical levitation loci for spheres on cryogenic fluids.

The conditions which allow a fluid to support a sphere having a higher specific gravity than its own are investigated. Three basic parameters which together define the maximum floating conditions are considered, including the Bond number, the wetting angle of the interface, and the ratio of solid-liquid specific gravities. The Bond number represents the ratio of buoyancy to surface tension forces. An analysis of the forces at the sphere-liquid interface is conducted to determine the optimum levitation loci, that is, the conditions permitting flotation of a maximum density sphere. Data for glycerine, carbon tetrachloride, and water spheres floating on a liquid nitrogen surface appear to be in good agreement with the analysis. Data for Teflon spheres on water also appear to be in agreement with the analytical results.

Hendricks, R. C.↗