The configuration evolution and macroscopic elasticity of fluid-filled closed cell composites : micromechanics and multiscale homogenization modelling

For fluid-filled closed cell composites widely distributed in nature, the configuration evolution and effective elastic properties are investigated using a micromechanical model and a multiscale homogenization theory, in which the effect of initial fluid pressure is considered. Based on the configuration evolution of the composite, we present a novel micromechanics model to examine the interactions between the initial fluid pressure and the macroscopic elasticity of the material. In this model, the initial fluid pressure of the closed cells and the corresponding configuration can be produced by applying an eigenstrain at the introduced fictitious stress-free configuration, and the pressure-induced initial microscopic strain is derived. Through a configuration analysis, we find the initial fluid pressure has a prominent effect on the effective elastic properties of freestanding materials containing pressurized fluid pores, and a new explicit expression of effective moduli is then given in terms of the initial fluid pressure. Meanwhile, the classical multiscale homogenization theory for calculating the effective moduli of a periodical heterogeneous material is generalized to include the pressurized fluid "inclusion" effect. Considering the coupling between matrix deformation and fluid pressure in closed cells, the multiscale homogenization method is utilized to numerically determine the macroscopic elastic properties of such composites at the unit cell level with specific boundary conditions. The present micromechanical model and multiscale homogenization method are illustrated by several numerical examples for validation purposes, and good agreements are achieved. The results show that the initial pressure of the fluid phase can strengthen overall effective bulk modulus but has no contribution to the shear modulus of fluid-filled closed cell composites.

Analytic prediction of structural stress-strain relations of microstructured metal

Nanostructured and ultra-fine grained metals have higher strength but extremely limited ductility compared to coarse grained metals. However, their ductility can be greatly improved by introducing a specific range of grain sizes in the microstructures. In the paper, multiscale unit cell approach (UCA) is developed and applied to predict the averaged stress-strain relations of the multiscale microstructure metals. The unit cell models are three-phase structured at different scale lengths of 100 nm, 1 μm and 10 μm with different volume fractions and periodic boundary conditions. The contributions of multi-scale microstructures to the macroscopic structural properties of metals are also studied using a analytic approach—two-step mean-field method (TSMF), where three microstructural parameters are introduced and thus mechanical properties such as strength and ductility are presented as a function of these parameters. For verification of these proposed numerical and theoretical algorithms, the structural properties of the pure nickel with three-grain microstructures are studied and the results from FEA and the proposed theory have good agreement.

Localized relaxational dynamics of succinonitrile

Succinonitrile (N≡C—CH₂—CH₂—C≡N) is a good ionic conductor, when doped with an ionic compound, at room temperature, where it is in its plastic crystalline phase (Long et al. Solid State Ionics 2003, 161, 105; Alarco et al. Nat. Mater. 2004, 3, 476). We report on the relaxational dynamics of the plastic phase near the two first-order phase transitions and on the effect of dissolving a salt in the plastic matrix by quasi-elastic neutron scattering. At 240 K, the three observed relaxations are localized and we can describe their dynamics (τ ≈ 1.7, 17, and 140 ps) to a certain extent from a model using a single molecule that was proposed by B_ée et al. allowing for all conformations in its unit cell (space group IM3M). The extent of the localized motion as observed is however larger than that predicted by the model and suggests that the isomerization of succinonitrile is correlated with a jump to the nearest neighbor site in the unit cell. The salt containing system is known to be a good ionic conductor, and our results show that the effect of the ions on the succinonitrile matrix is homogeneous. Because the isomerizations and rotations are governed by intermolecular interactions, the dissolved ions have an effect over an extended range. Due to the addition of the salt, the dynamics of one of the components (τ ≈ 17 ps) shows more diffusive character at 300 K. The calculated upper limit of the corresponding diffusion constant of succinonitrile in the electrolyte is a factor 30 higher than what is reported for the ions. Our results suggest that the succinonitrile diffusion is caused by nearest neighbor jumps that are localized on the observed length and time scales.

Towards elucidating microscopic structural changes in Li-ion conductors Li1+yTi2–yAly[PO4 ]3 and Li1+yTi2–yAly[PO4 ]3–x [MO4 ]x(M=V and Nb) : X-ray and27Al and31P NMR studies

A combination of X-ray powder diffraction (XRD) and nuclear magnetic resonance (NMR) studies has demonstrated that attempted substitutions of Al, V and Nb into the framework of LiTi₂(PO₄)₃ yield several impurity phases in addition to direct substitutions of Al into Ti and V, Nb into P sites. Direct substitutions were confirmed by changes in the unit cell dimensions as indicated by the peak shifts observed in the X-ray diffractographs and by analyses of the ²⁷Al and ³¹P magic angle spinning (MAS) spectra. A major impurity phase was identified as AlPO₄ (found in at least two polymorphs) and the amount present increases with increasing Al additions. The formation of AlPO₄ appeared to be enhanced by further V but suppressed by Nb substitution. These results suggest that the presence of AlPO₄ , together with the non-stoichiometric modified LTP, may be the cause for the observed densification of this material upon sintering and the increased ionic conductivity.

Atomic scale simulation of deformation in magnesium single crystals

The deformation behaviour of magnesium single crystals under plane strain conditions has been examined using molecular dynamics modelling. The simulations were based on an existing atomic potential for magnesium taken from the literature. A strain of 10% was applied at rates of 3x10⁹s^-1 and 3x10⁷s^-1. The simulations predicted the formation of mechanical twins that accommodated extension in the c-axis direction of the hexagonal unit cell. However, the predicted twin is not of the same kind found in magnesium, but is that commonly observed in titanium. It is believed that further analysis of the physical properties predicted by this interatomic potential will shed more light on the atomic processes controlling twinning in Magnesium alloys. It also highlights the need for improvements to the interatomic potential such that more accurate deformation behaviour can be attained.

A new solution method for homogenization of effective properties of electromagnetic honeycombs

In this paper, an analytical model and its new numerical solution using the homogenization method are developed to determine the effective electromagnetic characteristics of honeycombs. Based on the proposed solution method, the electromagnetic properties are obtained by employing the multi-scale homogenization theory and periodical electric (magnetic) potential boundary conditions. Further, the effect of geometry of honeycomb's unit cell on effective electromagnetic properties is investigated with the use of the proposed method. The numerical results are compared with analytic results using the Smith-Scarpa's semi-empirical formula.

On the effective mechanical properties of fluid-saturated composites : a homogenization approach

Composites containing saturated fluid are widely distributed in nature, such as saturated rocks, colloidal materials and biological cells. In the study to determine effective mechanical properties of fluid-saturated composites, a micromechanical model and a multi-scale homogenization-based model are developed. In the micromechanical model the internal fluid pressure is generated by applying eigenstrains in the domain of the fluid phase and the explicit expressions of effective bulk modulus and shear modulus are obtained. Meanwhile a multi-scale homogenization theory is employed to develop the homogenization-based model on determination of effective properties at the small scale in a unit cell level. Applying the two proposed approaches, the effects of the internal pressure of hydrostatic fluid on effective properties are further investigated.

In-situ dehydration studies of fully K-, Rb-, and Cs-exchanged natrolites

In-situ synchrotron X-ray powder diffraction studies of K-, Rb-, and Cs-exchanged natrolites between room temperature and 425 °C revealed that the dehydrated phases with collapsed frameworks start to form at 175, 150, and 100 °C, respectively. The degree of the framework collapse indicated by the unit-cell volume contraction depends on the size of the non-framework cation: K-exchanged natrolite undergoes an 18.8% unit-cell volume contraction when dehydrated at 175 °C, whereas Rb- and Cs-exchanged natrolites show unit-cell volume contractions of 18.5 and 15.2% at 150 and 100 °C, respectively. In the hydrated phases, the dehydration-induced unit-cell volume reduction diminishes as the cation size increases and reveals increasingly a negative slope as smaller cations are substituted into the pores of the natrolite structure. The thermal expansion of the unit-cell volumes of the dehydrated K-, Rb-, and Cs-phases have positive thermal expansion coefficients of 8.80 × 10⁻⁵ K⁻¹, 1.03 × 10⁻⁴ K⁻¹, and 5.06 × 10⁻⁵ K⁻¹, respectively. Rietveld structure refinements of the dehydrated phases at 400 °C reveal that the framework collapses are due to an increase of the chain rotation angles, ψ, which narrow the channels to a more elliptical shape. Compared to their respective hydrated structures at ambient conditions, the dehydrated K-exchanged natrolite at 400 °C shows a 2.2-fold increase in ψ, whereas the dehydrated Rb- and Cs-natrolites at 400 °C reveal increases of ψ by ca. 3.7 and 7.3 times, respectively. The elliptical channel openings of the dehydrated K-, Rb-, to Cs-phases become larger as the cation size increases. The disordered non-framework cations in the hydrated K-, Rb-, and Cs-natrolite order during dehydration and the subsequent framework collapse. The dehydrated phases of Rb- and Cs-natrolite can be stabilized at ambient conditions.

Immobilization of large, aliovalent cations in the small-pore zeolite K-natrolite by means of pressure

High-pressure ion exchange of small-pore zeolite K-natrolite allows immobilization of nominally non-exchangeable aliovalent cations such as trivalent europium. A sample exchanged at 3.0(1) GPa and 250 °C contains about 4.7 Eu^III ions per unit cell, which is equivalent to over 90 % of the K⁺ cations being exchanged.

Pressure- and heat-induced insertion of CO2 into an auxetic small-pore zeolite

When the small-pore zeolite natrolite is compressed at ca. 1.5 GPa and heated to ca. 110 °C in the presence of CO₂, the unit cell volume of natrolite expands by 6.8% and ca. 12 wt % of CO₂ is contained in the expanded elliptical channels. This CO₂ insertion into natrolite is found to be reversible upon pressure release.

Monte Carlo calculations of the free energy of binary SII hydrogen clathrate hydrates for identifying efficient promoter molecules

The thermodynamics of binary sII hydrogen clathrates with secondary guest molecules is studied with Monte Carlo simulations. The small cages of the sII unit cell are occupied by one H2 guest molecule. Different promoter molecules entrapped in the large cages are considered. Simulations are conducted at a pressure of 1000 atm in a temperature range of 233?293 K. To determine the stabilizing effect of different promoter molecules on the clathrate, the Gibbs free energy of fully and partially occupied sII hydrogen clathrates are calculated. Our aim is to predict what would be an efficient promoter molecule using properties such as size, dipole moment, and hydrogen bonding capability. The gas clathrate configurational and free energies are compared. The entropy makes a considerable contribution to the free energy and should be taken into account in determining stability conditions of binary sII hydrogen clathrates.

Cyclic carbonate–sodium smectite intercalates

Five-membered cyclic organic carbonates (COC) are of interest for their ability to modify the surface properties of smectites and enhance the hydraulic resistance of bentonites to saline leachates. The mechanism of interaction of glycerol carbonate (GC) and several other hydroxyl containing cyclic organic carbonates (generally having progressively greater molecular masses) with sodium montmorillonite (Na+-Mt) was studied using powder X-ray diffraction and infrared spectroscopy. The 001 reflection for GC/Na+-Mt intercalates varied with the amount COC added, and the measured d001 value increased from 1.29 nm to as large as 2.22 nm at equal-mass coverage of the COC to Na+-Mt. In general, when intercalated, the cyclic carbonyl (Cdouble bond; length as m-dashO) stretch and the fundamental hydroxyl (O–H) stretch bands of COC derivatives were red-shifted with respect to these bands for neat COC, indicating strong ion-dipole interaction of the carbonyl group with interlayer Na+, and H-bonding of the OH group with both interlayer water and Mt surfaces. A stable and highly ordered intercalate was produced at a 1:1 mass loading with Mt in which about 6 GC molecules per unit cell (~ 7 molecules per Na+ ion) replaced most of the interlayer water.

EBSD and AFM observations of the microstructural changes induced by low temperature plasma carburising on AISI 316

Low temperature plasma carburising (LTPC) has been increasingly accepted as a hardening process for austenitic stainless steels because it produces a good combination of tribological and corrosion properties. The hardening mechanism is based on the supersaturation of the austenitic structure with carbon, which greatly hardens the material, significantly expands the fcc unit cell, produces high levels of compressive residual stresses and, ultimately, leads to the occurrence of deformation bands and rotation of the crystal lattice. The microstructural changes introduced during plasma carburising have a significant impact on the mechanical, tribological and corrosion performance and, for this reason, the microstructure of expanded austenite or S-phase has been extensively studied. However, modern surface characterisation techniques could provide new insights into the formation mechanism of S-phase layers. In this work, backscattered electron diffraction and atomic force microscopy were used to characterise the surface layers of expanded austenite produced by LTPC in an active screen furnace. Based on the experimental results, the plastic deformation, its dependence on crystallographic orientation, the evolution of grain boundaries, and their effects on mechanical, tribological and corrosion properties are discussed. © 2011 Elsevier B.V. All rights reserved.

Metallic ternary telluride with sphalerite superstructure

A new ternary compound with composition Cu5Sn2Te7 has been synthesized using the stoichiometric reaction of Cu, Sn, and Te. The compound crystallizes in C2 space group with unit cell parameters of a = 13.549(2) Å, b = 6.0521(11) Å, c = 9.568(2) Å, and β = 98.121(2)°. Cu5Sn2Te7 is a superstructure of sphalerite and exhibits tetrahedral coordination of Cu, Sn, and Te atoms, containing a unique adamantane-like arrangement. The compound is formally mixed valent with a high electrical conductivity of 9.8 × 10(5) S m(-1) at 300 K and exhibits metallic behavior having p-type charge carriers as indicated from the positive Seebeck coefficient. Hall effect measurements further confirm holes as charge carriers with a carrier density of 1.39 × 10(21) cm(-3) and Hall mobility of 4.5 cm(2) V(-1) s(-1) at 300 K. The electronic band structure calculations indicate the presence of a finite density of states around the Fermi level and agree well with the p-type metallic conductivity. Band structure analysis suggests that the effective mass of the hole state is small and could be responsible for high electronic conductivity and Hall mobility. The high thermal conductivity of 15.1 W m(-1) K(-1) at 300 K coupled with the low Seebeck coefficient results in a poor thermoelectric figure of merit (ZT) for this compound. Theoretical calculations indicate that if Cu5Sn2Te7 is turned into a valence precise compound by substituting one Cu by a Zn, a semiconducting material, Cu4ZnSn2Te7, with a direct band gap of ∼ 0.5 eV can be obtained.