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The mean-field theory of dilute spin-glasses is studied in the limit where the average coordination number is finite. The zero-temperature phase diagram is calculated and the relationship between the spin-glass phase and the percolation transition is discussed. The present formalism is applicable also to graph optimization problems.
While changes in the coordination number for liquid silicon upon supercooling, signaling an underlying liquid-liquid phase transition, have been predicted, x-ray and neutron measurements have produced conflicting reports. In particular some studies have found an increase in the first shell coordination as temperature decreases in the supercooled regime, while others have reported increases in the coordination number with decreasing temperature. Employing the technique of electrostatic levitation coupled with high energy x-ray diffraction (125 keV), and rapid data acquisition (100ms collection times) using an area detector, we have obtained high quality structural data more deeply into the supercooled regime than has been possible before. No change in coordination number is observed in this temperature region, calling into question previous experimental claims of structural evidence for the existence of a liquid-liquid phase transition.
We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming constant coordination number. It obtains the most entropic density of single grain states, which predicts several observables including the distribution of contact forces. We compare these results against empirical data obtained in dynamic simulations of granular packings. The agreement between theory and the empirics is quite good, helping validate the use of statistical mechanics methods in granular physics. The differences between theory and empirics are mainly due to the variable coordination number, and when the empirical data are sorted by that number we obtain several insights that suggest an underlying elegance in the density of states
The three compounds Ga2Cl4(4-mepy)2 (1),[GaCl2(4-mepy)4]GaCl4x1/2(4-mepy); (2) and GaCl2(4-mepy)2(S2CNEt2); (3) (4-mepy= 4-methylpyridine) have been prepared from reactions of gallium (II) chloride in 4-methylpyridine and characterized by single-crystal X-ray analysis. Small variations in the reaction conditions for gallium(II) chloride can produce crystals with substantially different structural properties. The three compounds described here encompass a neutral gallium(II) dimer in which each gallium is four-coordinate, an ionic compound containing both anionic and cationic gallium complex ions with different coordination numbers and a neutral six-coordinate heteroleptic
Lanthanide abundance variation and coordination number, comparing abundances in terrestrial and meteoritic materials with average chondrite
A method is presented for numerical airfoil optimization whereby a reduced number of design coordinates are used to define the airfoil shape. The approach is to define the airfoil as a linear combination of shapes. These basic shapes may be analytically or numerically defined, allowing the designer to use his insight to propose candidate designs. The design problem becomes one of determining the participation of each such function in defining the optimum airfoil. Examples are presented for two-dimensional airfoil design and are compared with previous results based on a polynomial representation of the airfoil shape. Four existing NACA airfoils are used as basic shapes. Solutions equivalent to previous results are achieved with a factor of more than 3 improvements in efficiency, while superior designs are demonstrated with an efficiency greater than 2 over previous methods. With this shape definition, the optimization process is shown to exploit the simplifying assumptions in the inviscid aerodynamic analysis used here, thus demonstrating the need to use more advanced aerodynamics for airfoil optimization.
High-pressure infrared absorption spectra of alpha-quatz, coesite, stishovite, and SiO2 glass are consistent with the primary compression mechanism of the initially tetrahedrally bonded phases being the bending of the Si-O-Si angle at pressures less than 10-20 GPa. At higher pressures, up to 40 GPa, we observe a decline in the intensity of the infrared SiO4 asymmetric-stretching vibrations of all three phases, with an increase in the relative amplitude between 700 and 900/cm. This change in intensities is attributed to an increase in the average coordination number of silicon through extreme distortion of tetrahedra. At pressures above approximately 20 GPa, the low-pressure crystalline polymorphs gradually become amorphous, and the infrared spectra provide evidence for an increase in silicon coordination in these high-density amorphous phases. The pressure-amorphized samples prepared from quartz and coesite differ structurally both from each other and from silica glass that has been compressed, and the high pressure spectra indicate that these materials are considerably more disordered than stishovite under comparable pressure conditions. Average mode Grueneisen parameters calculated for quartz, stishovite and fused silica from both infrared and Raman spectra are compatible with the corresponding thermodynamic value of the Grueneisen parameter, however, that of coesite is significantly discrepant.
Determination of the oxidation state of iron in the plagioclase from the coarse-grained basalts 10044 and 12021, using Mossbauer spectroscopy. The location of iron in the crystal structure was also investigated. The spectra show that iron is in the high-spin ferrous state, and they located at least two distinct positions with different coordination numbers. Some excess resonant absorption is probably due to Fe(3+), although the Fe(3+) doublet could not be positively resolved.
X-ray electron spectra were obtained of the 2p-levels of Fe, Ti, Si, Al, and Mg, and of the 1s-level in lunar regolith from the Sea of Fertility and the Sea of Tranquillity. The spectra of the same elements were recorded for approximately 30 rock forming minerals, oceanic gabbro, meteoritic eucrite, and several iron meteorites. Analysis of the results based on line positions showed that all the elements studied have the usual degrees of oxidation, and that oxygen atoms are their nearest neighbors. The predominant coordination number of Al is 4. Analysis and comparison of the Fe2p spectra in regolith, various iron meteorites, and stainless steel leads to these conclusions: Metallic iron in lunar regolith is in a highly dispersed state and is unusually stable with respect to oxidation by the oxygen of the earth's atmosphere.
Shock recovery experiments performed on Riverside nontronite cause a marked color change in the clay, from olive-yellow to strong brown upon recovery from shock loading to peak pressures of 180 to 300 kbar. This color change spans the color range observed in the fine material at the Viking lander sites. The change in color is attributed to a shift in the O(2-)-Fe(3+) charge transfer bands to longer wavelengths, which causes the material to become both redder and darker. The observations that the color change is associated with the dehydroxylation of the clay and the Moessbauer spectra that reveal a lowering of the coordination number of the Fe(3+) as the OH(-) is removed from the structure are seen as suggesting that the movement of the absorption bands into the visible is caused by the formation of 4-fold or distorted 5-fold-like Fe(3+) within the octahedral layers of the clay.
Superior SiC characteristics can be achieved through the use of ideal constituent powders and careful post-synthesis processing steps. High purity SiC powders of approx. 1000 A uniform diameter, nonagglomerated and spherical were produced. This required major revision of the particle formation and growth model from one based on classical nucleation and growth to one based on collision and coalescence of Si particles followed by their carburization. Dispersions based on pure organic solvents as well as steric stabilization were investigated. Although stable dispersions were formed by both, subsequent part fabrication emphasized the pure solvents since fewer problems with drying and residuals of the high purity particles were anticipated. Test parts were made by the colloidal pressing technique; both liquid filtration and consolidation (rearrangement) stages were modeled. Green densities corresponding to a random close packed structure (approx. 63%) were achieved; this highly perfect structure has a high, uniform coordination number (greater than 11) approaching the quality of an ordered structure without introducing domain boundary effects. After drying, parts were densified at temperatures ranging from 1800 to 2100 C. Optimum densification temperatures will probably be in the 1900 to 2000 C range based on these preliminary results which showed that 2050 C samples had experienced substantial grain growth. Although overfired, the 2050 C samples exhibited excellent mechanical properties. Biaxial tensile strengths up to 714 MPa and Vickers hardness values of 2430 kg/sq mm 2 were both more typical of hot pressed than sintered SiC. Both result from the absence of large defects and the confinement of residual porosity (less than 2.5%) to small diameter, uniformly distributed pores.
Extended X ray absorption fine structure (EXAFS) is a powerful technique for probing the local atomic structure of battery and fuel cell materials. The major advantages of EXAFS are that both the probe and the signal are X rays and the technique is element selective and applicable to all states of matter. This permits in situ studies of electrodes and determination of the structure of single components in composite electrodes, or even complete cells. EXAFS specifically probes short range order and yields coordination numbers, bond distances, and chemical identity of nearest neighbors. Thus, it is ideal for structural studies of ions in solution and the poorly crystallized materials that are often the active materials or catalysts in batteries and fuel cells. Studies on typical battery and fuel cell components are used to describe the technique and the capability of EXAFS as a structural tool in these applications. Typical experimental and data analysis procedures are outlined. The advantages and limitations of the technique are also briefly discussed.
The dependence of primary arm spacings on growth speed was investigated for cellular and dendritic arrays in Pb-10 wt percent Sn samples directionally solidified under a constant positive thermal gradient in the melt. The gradient of constitutional supercooling was varied from almost zero (near the break-down of the planar liquid-solid interface at small growth speeds, cellular morphology) to near unity (large growth speeds, dendritic morphology). The spatial arrangements of cells and dendrites, as given by their coordination number, are not very different from each other. It appears that primary arm spacing maxima and the cell to dendrite transition are strongly influenced by the magnitude of the solute partition coefficient. The planar to cellular bifurcation is supercritical in Pb-Sn which has a high partition coefficient, as compared to the subcritical behavior reported in Al-Cu and succinonitrile-acetone, both of which have low partition coefficients. The primary arm spacing model due to Hunt agrees with the experimentally observed trend for the whole growth regime. There is a good quantitative agreement at higher gradients of supercooling. However, the model overpredicts the primary arm spacings at low gradients of constitutional supercooling.
The dependence of primary arm spacings on growth speed was investigated for cellular and dendritic arrays in Pb-10 wt percent Sn samples directionally solidified under a constant positive thermal gradient in the melt. The gradient of constitutional supercooling was varied from almost zero (near the break-down of the planar liquid-solid interface at small growth speeds, cellular morphology) to near unity (large growth speeds, dendritic morphology). The spatial arrangements of cells and dendrites, as given by their coordination number, are not very different from each other. It appears that primary arm spacing maxima and the cell to dendrite transition are strongly influenced by the magnitude of the solute partition coefficient. The planar to cellular bifurction is supercritical in Pb-Sn which has a high partition coefficient, as compared to the subcritical behavior reported in Al-Cu and succinonitrile-acetone, both of which have low partition coefficients. The primary arm spacing model due to Hunt agrees with the experimentally observed trend for the whole growth regime. There is a good quantitative agreement at higher grdients of supercooling. However, the model overpredicts the primary arm spacings at low gradients of constitutional supercooling.
The dependence of primary arm spacings on growth speed has been investigated for cellular and dendritic arrays in directionally solidified Pb-10 wt pct Sn. The spatial arrangements of cells and dendrites, as given by their coordination number, are not very different from each other. The primary arm spacing maxima and the cell-to-dendrite transition appear to be strongly influenced by the magnitude of the solute partition coefficient (k). The planar-to-cellular transition in Pb-Sn (k = 0.50) is supercritical as compared to the subcritical behavior reported in Al-Cu (k = 0.14) and succinonitrile-acetone (k = 0.1).
The geometrical structures of M(+) (Ar)n ions, with n = 1-14, have been studied by the minimization of a many-body potential surface with a simulated annealing procedure. The minimization method is justified for finite systems through the use of an information theory approach. It is carried out for eight potential-energy surfaces constructed with two- and three-body terms parametrized from experimental data and ab initio results. The potentials should be representative of clusters of argon atoms with first-row transition-metal monocations of varying size. The calculated geometries for M(+) = Co(+) and V(+) possess radial shells with small (ca. 4-8) first-shell coordination number. The inclusion of an ion-induced-dipole-ion-induced-dipole interaction between argon atoms raises the energy and generally lowers the symmetry of the cluster by promoting incomplete shell closure. Rotational constants as well as electric dipole and quadrupole moments are quoted for the Co(+) (Ar)n and V(+) (Ar)n predicted structures.
Lanthanide metal ions were incorporated into the polyimide derived from 2,2-bis(3,4-dicarboxyphenyl) hexafluoropropane dianhydride (6FDA) and 1,3-bis(aminophenoxy) benzene (APB) in an attempt to produce molecular level metal-polymer composites. The lanthanide series of metal ions (including aluminum, scandium, and yttrium) provide discrete and stable metal ions in the 3+ oxidation state. Throughout the series there is a uniform variation in ionic size ranging from 50 pm for aluminum to a maximum of 103.4 pm for cerium and gradually decreasing again to 84.8 pm for lutetium. The high charge-to-size ratio for these ions as well as the ability to obtain large coordination numbers makes them excellent candidates for interacting with the polymer substructure. The distinct lack of solubility of simple lanthanide salts such as the acetates and halides has made it difficult to obtain metal ions distributed in the polymer framework as discrete ions or metal complexes rather than microcomposites of metal clusters. (Lanthanum nitrates are quite soluble, but the presence of the strongly oxidizing nitrate ion leads to serious degradation of the polymer upon thermal curing. This work was successful at extending the range of soluble metals salts by using chelating agents derived from the beta-diketones dipivaloylmethane, dibenzoylmethane, trifluoroacetylacetone, and hexafluoroacetylacetone. Metal acetates which are insoluble in dimethylacetamide dissolve readily in the presence of the diketones. Addition of the polyimide yields a homogeneous resin which is then cast into a clear film. Upon curing clear films were obtained with the dibenzoylmethane and trifluoroacetylacetone ligands. The dipavaloylmethane precipitates the metal during the film casting process, and hexafluoroacetylacetone gives cured films which are deformed and brittle. These clear films are being evaluated for the effect of the metal ions on the coefficient of thermal expansion, resistance to atomic oxygen, and on selective gas permeability. Much more commonly than above, polyimide films are prepared by casting the film as the poly(amic acid) precursor which is then converted to the imidized form during the thermal cure cycle. Very limited success was achieved in the past in adding lanthanide metal ions to the amide precursors because of gellation and lack of solubility. With the use of the diketone ligands cited above, the solubility and gellation problems were overcome. However, the films after curing were clear but unacceptably brittle. Attempts to overcome this cure embrittlement problem are in progress.
For nearly 40 yr, studies of exosphere formation on airless bodies have been hindered by uncertainties in our understanding of the underlying ion collisional sputtering by the solar wind (SW). These ion impacts on airless bodies play an important role in altering their surface properties and surrounding environment. Much of the collisional sputtering data needed for exosphere studies come from binary collision approximation (BCA) sputtering models. These depend on the surface binding energy (SBE) for the atoms sputtered from the impacted material. However, the SBE is not reliably known for many materials important for planetary science, such as plagioclase feldspars and sodium pyroxenes. BCA models typically approximate the SBE using the cohesive energy for a monoelemental solid. We use molecular dynamics (MD) to provide the first accurate SBE data we are aware of for Na sputtered from the above silicate minerals, which are expected to be important for exospheric formation at Mercury and the Moon. The MD SBE values are ∼8 times larger than the Na monoelemental cohesive energy. This has a significant effect on the predicted SW ion sputtering yield and energy distribution of Na and the formation of the corresponding Na exosphere. We also find that the SBE is correlated with the coordination number of the Na atoms within the substrate and with the cohesive energy of the Na-bearing silicate. Our MD SBE results will enable more accurate BCA predictions for the SW ion sputtering contribution to the Na exosphere of Mercury and the Moon.