Fractal structure and optical properties of semicontinuous silver films

Semicontinuous silver films, prepared by vacuum evaporation on substrate of KBr crystals, have been made with area coverage in the range 0.3–0.8. The morphology of the films were found to change with coverage p. At small or large coverage range, homogeneous films were observed, but when the coverage approaches a critical value p_c (p_c ≈ 0.65), the film was inhomogeneous. The topologic parameters of films such as mean size of cluster S_AV, correlation length ξ and fractal dimension D_f were measured. When the area coverage was close to p_c, S_AV and ξ rapidly diverged and a knee point appeared in the curve of D_f vs. p. The transmittance of films in mid-infrared wave-band (2.5–12.5 m) was measured. For homogeneous films, as wavelength increased, transmittance increased when p < p_c but decreased when p < p_c. On the other hand, transmittance was wavelength independent for inhomogeneous films. The optical percolation phenomenon is observed at a region where the fractal dimension D_f of the film was kept approximately constant while correlation length diverges. These experimental results were compared with existing theory and we interpret the effect of deposition and coalescence on the percolation parameters by considering the growth mechanism of a nano-structured metal film.     

The influence of the stress state on the plastic zone size

“Linear elastic” fracture mechanics is based on the “plane strain” condition which means dε_zz = 0. Really stress states can occur in structures or components where dε_zz > 0. Two examples are discussed. Using the v. Mises criterion and the Sneddon equations the influence of an external stress σ^e_zz acting parallel to the crack front on the plastic zone size is calculated and demonstrated by examples.     

Effects of microstructural variables on the deformation behaviour of dual-phase steel

An expression for the stress of martensite in dual-phase steel was developed, which shows the interdependence of the stress of martensite and strain hardening in the ferrite matrix and the contribution of microstructural variables (the volume fraction of martensite f_m, ferrite grain size d_f, and martensite particle size d_m). The onset of plastic deformation of martensite in dual-phase steel was predicted to depend on its yield strength and the microstructural variables, and this was verified by the modified Crussard-Jaoul analysis. It was found that for this dual-phase steel, refining the grain size and increasing f_m increase the flow stress and raise the strain hardening rate at low strains, but little affect the strain hardening rate at high strains. The effect of the ferrite grain size on the flow stress of this dual-phase steel was found to obey the Hall-Petch relation, i.e. σ = σ₀^e + K^ed_f^−1/2, where the Hall-Petch intersection σ₀^e and slope K^e are functions of strain, f_m and d_m. The effects of the plastic deformation of martensite and the microstructural variables on the strain hardening rate and the Hall-Petch behaviour were analysed in terms of the densities of statistically stored dislocations and geometrically necessary dislocations using the previously developed theoretical model.     

The dynamic elastic buckling of a circular arch with finite displacements and initial imperfections

The equilibrium equations for elastic circular arches are established using the principle of virtual work. The nonlinear partial differential equations of motion are solved using a finite difference method (Park's method for time difference). The dynamic stability of a hinged and a clamped elastic circular arch with a uniform step load is analysed with finite deformations and initial geometric imperfections. Results show that the buckling mode varies with the value of the arch half angle, θ₀. The boundary condition and initial imperfection amplitude also effect the buckling mode. A nearly perfect arch usually buckling with a “direct” buckling form, while an imperfect arch with an “indirect” buckling form. The effect of θ₀ on the ratio p_d/p_s (p_d is the dynamic critical load and p_s the static critical load) is shown for different initial imperfections and different boundary conditions.     

Validation and calibration of a lateral confinement model for long-rod penetration at ordnance and high velocities

In designing targets for laboratory long-rod penetration tests, the question of lateral confinement often arises, “How wide should the target be to exert enough confinement?” For ceramic targets, the problem is enhanced as ceramics are usually weak in tension and therefore have less self-confinement capability. At high velocities the problem is enhanced even more as the crater radius and the extent of the plastic zone around it are larger. Recently we used the quasistatic cavity expansion model to estimate the resistance of ceramic targets and its dependence on impact velocity [1]. We validated the model by comparing it to computer simulations in which we used the same strength model. Here we use the same approach to address the problem of lateral confinement.

We solved the quasistatic cavity expansion problem in a cylinder with a finite outside radius “b” at which σ_r (b) = 0 (σ_r = radial stress component). We did this for three cases: ceramic targets, metal targets, and ceramic targets confined in a metal casing. Generally, σ_r (a) is a decreasing function of “a” (“a” = expanding cavity radius, and σ_r (a) = the stress needed to continue opening the cavity). In the usual cavity expansion problem b → ∞, σ_r (a) = const., R =−σ_r (a) (R = resistance to penetration). For finite “b” we estimate R by averaging σ_r (a) over a range o ≤ a ≤ a_r, (where a_r, the upper bound of the range, is calibrated from computer simulations).

We ran 14 computer simulations with the CTH wavecode and used the results to calibrate a_r for the different cases and to establish the overall validity of our approach.

We show that generally for D_t/D_p > 30, the degree of confinement is higher than 95% (D_t = target diameter; D_p = projectile diameter; and degree of CONFINEMENT = R/R_∞; R∞ = resistance of a laterally infinite target). We also show the tensile strength of ceramic targets (represented by the spall strength P_min) has a significant effect on the degree of confinement, while other material parameters have only a minor effect.     

Magnetism of epitaxial Ru and Rh monolayers on graphite

Recently, Pfandzelter et al. (1995) reported the first observation of monolayer ferromagnetism of a 4d metal, namely in a Ru monolayer grown on graphite. Using the tight-binding linear-muffin-tin-orbital (TB-LMTO) method we have calculated the electronic and magnetic structure of epitaxial Ru and Rh monolayers on graphite with the experimentally determined atomic density. Monolayers of the other 4d elements were found to be non-magnetic already in the free-standing limit. The magnetic structure of the Ru and Rh monolayers is studied as a function of metal-graphite interlayer distance h. They become magnetic at h = 4.5 a.u. (Ru) and h = 4.8 a.u. (Rh) in a first-order transition. In the assumed p(2 × 2) super-structure, the moments on the “hollow” site atoms are up to four times bigger than those on the “on-top” site atoms. For h > 5.4 a.u. (Ru) and h > 5.1 a.u. (Rh) the site dependence vanishes and the moments of the free monolayers are approximately reached (1.9 μ_B and 1.2 μ_B, respectively).     

Fracture mechanisms of ceramic coating during wear

A typical buckling phenomenon of the coating on the wear groove caused by the residual compressed stress was analyzed by the interface fracture mechanics and the buckling theory. It has been found that there is a critical thickness of coating on the wear groove for the buckling. The critical thickness can be calculated by t_b/c_d = [12(1 − v²_f)σ_R/π²E_f]1/2 (here t_b is the coating thickness, c_d the length of the interfacial crack, v_f the Poisson's ratio of the coating, σ_R the residual compressed stress in the coating, and E_f the elastic modulus of the coating).     

The neutron EDM experiment at the ILL

The latest-generation neutron electric dipole moment (EDM) experiment has been collecting data at the ILL since 1996. It uses a “cohabiting” atomic-mercury magnetometer to measure and compensate for the magnetic field fluctuations that were the principal source of systematic errors in previous experiments. The first results, which are soon to be published, essentially verify the existing limit on the dipole moment d_n; however, this new measurement is clearly limited by statistical rather than systematic uncertainties.     

Addition of “Living” Polymers onto C60.

Various “living” polymers were grafted onto C₆₀ The number of arms of the so obtained “star” molecules can be controlled by stoechiometry and/or by varying the reactivity of the carbanion on the “living” chain against a double bond on the C₆₀. Even the oxanion of “living” polyethylenoxide is able to add onto the reactive double bonds on C₆₀. In some conditions, the carbanions present on these alkaline salts of grafted fullerenes becomes able to initiate anionic polymerization of vinyl monomers. Using “living” poly(phenylvinylsulfoxide) as a precursor polymer for PA, polyacetylene chains could be attached to the fullerene.     

An efficient method for reliability evaluation of multistate networks given all minimal path vectors

The multistate networks under consideration consist of a source node, a sink node, and some independent failure-prone components in between the nodes. The components can work at different levels of capacity. For such a network, we are interested in evaluating the probability that the flow from the source node to the sink node is equal to or greater than a demanded flow of d units. A general method for reliability evaluation of such multistate networks is using minimal path (cut) vectors. A minimal path vector to system state d is called a d-MP. Approaches for generating all d-MPs have been reported. Given that all d-MPs have been found, the issue becomes how to evaluate the probability of the union of the events that the component state vector is greater than or equal to at least one of the d-MPs. There is a need for a more efficient method of determining the probability of this union of events. In this paper, we report an efficient recursive algorithm for this union probability evaluation based on the Sum of Disjoint Products (SDP) principle, and name it the Recursive Sum of Disjoint Products (RSDP) algorithm. The basic idea is that, based on the SDP principle and a specially defined “maximum” operator, “⊕”, the probability of a union with L vectors can be calculated via calculating the probabilities of several unions with L-1 vectors or less. The correctness of RSDP is illustrated. The efficiency of this algorithm is investigated by comparing it with an existing algorithm that is generally accepted to be efficient. It is found that RSDP is more efficient than the existing algorithm when the number of components of a system is not too small. RSDP provides us with an efficient, systematic and simple approach for evaluating multistate network reliability given all d-MPs.     

A dynamic measure of order in structural glasses

Although some patterns of physical behavior are common in the glass transition and in the properties of supercooled liquids and glasses (characteristic viscoelasticity, temperature dependence of viscosity and relaxation times, property evolution through “physical aging”, difficulties in performing equilibrium measurements or simulations, etc.), it is difficult to arrive at a definition of the glass transition which distinguishes it from other phenomena exhibiting similar features. The present paper addresses this problem by defining a dynamical measure of order involving the average “shape” of particle trajectories in supercooled liquids. This dynamic order parameter should provide a measure of “closeness” to the glass transition and some indirect insights into the physical nature of supercooled liquids and glasses. Arguments are given that the proposed dynamic measure of order [“generalized capacity”, C(T)] is related to the temperature-dependent “effective hydrodynamic radius” R_H(T) measured in supercooled liquids and model numerical calculations are given to support this view. Some consequences of the intermittent particle motion at low temperatures for stress relaxation are also discussed.     

A mechanistic model for the effect of stress ratio on the LEFM fatigue crack growth behavior of metals and alloys—II. Crack-brittle materials

A recently proposed mechanistic model for the effect of stress ratio, R, on the LEFM (long) fatigue crack growth behavior of “crack-ductile” materials is extended here to explain and predict similar behavior under similar conditions of “crack-brittle” materials characterised by the presence of “static” modes of fatigue fracture in stages II and III. It is shown that in these materials the stage I behavior is similar, but the stages II and III behave differently from crack-ductile materials. Mechanism-based existence of two types of stage II curves characterised respectively by “ pure shear mode ” (SM-II) and “mixed-mode” (MM-II), both plotting linear but having different slopes, is introduced. It is shown that while stage SM-II is insensitive, stage MM-II is significantly sensitive to R, in the same material. Similar to stage I, another “ moving pivot-point ” exists at the transition from SM-II to MM-II, which slides down the “ master shear-curve ” with increasing R. Assuming a critical K_max for the initiation of static modes, a critical R for saturation of these modes, and Paris-type growth relations, a quantitative predictive model containing growth equations for stages SM-II and MM-II, has been developed. Stage III is discussed only qualitatively. Reasonably good agreement was found between predicted curves at selected R-values and a relatively large volume of experimental data for steels, Al-alloys and Ti-alloys. This simple, alternative model may be used for obtaining quick, fairly accurate and conservative estimates of R-influenced crack growth rates for design applications in preference to crack-closure which frequently requires elaborate and tedious experimental procedures.     

Sorbitan ester organogels for transdermal delivery of sumatriptan

The partial phase behavior, rheological, and drug release characteristics of an organogel (OG) composed of water, isooctane and sorbitan esters, sorbitan monopalmitate (Span-40) and poly(oxyethylene)sorbitan monostearate (Polysorbate-60) were studied. Phase diagrams showed decreasing areas of optically isotropic organogel region depending on the surfactant ratio, K_w and drug incorporation. The nonbirefringent, clear isotropic solution suggested the reverse micellar/microemulsion nature of the organogel without any molecular ordering. The increase in drug concentration in OGs leads to increase in the viscosity and sol-gel transition temperature (T_g). Fractal dimension (d_f) values calculated for different compositions suggested that the density of the tubular network increases with increasing drug concentration in OGs. The release rate of the drug from OGs was found to be non-Fickian through the dialysis membrane. The permeation rate of sumatriptan from pig skin was 0.231 mg/h/cm² (781.9 nmol/h/cm²). The study indicates potential of OG as a reservoir system for transdermal drug delivery.     

Sintering behavior and microwave dielectric properties of Bi3(Nb1−xTax)O7 solid solutions

Solid solutions of Bi₃(Nb_1−xTa_x)O₇ (x = 0.0, 0.3, 0.7, 1) were synthesized using solid state reaction method and their microwave dielectric properties were first reported. Pure phase of fluorite-type could be obtained after calcined at 700 °C (2 h)⁻¹ between 0 ≤ x ≤ 1 and Bi₃(Nb_1−xTa_x)O₇ ceramics could be well densified below 990 °C. As x increased from 0.0 to 1.0, saturated density of Bi₃(Nb_1−xTa_x)O₇ ceramics increased from 8.2 to 9.1 g cm⁻³, microwave permittivity decreased from 95 to 65 while Q_f values increasing from 230 to 560 GHz. Substitution of Ta for Nb modified temperature coefficient of resonant frequency τ_f from −113 ppm °C⁻¹ of Bi₃NbO₇ to −70 ppm °C⁻¹ of Bi₃TaO₇. Microwave permittivity, Q_f values and τ_f values were found to correlate strongly with the structure parameters of fluorite solid solutions and the correlation between them was discussed in detail. Considering the low densified temperature and good microwave dielectric proprieties, solid solutions of Bi₃(Nb_1−xTa_x)O₇ ceramics could be a good candidate for low temperature co-fired ceramics application.     

A generalized multistate-based path vector approach to multistate two-terminal reliability

The two-terminal reliability problem assumes that a network and its elements are either in a working or a failed state. However, many practical networks are built of elements that may operate in more than two states i.e., elements may be degraded but still functional. Multistate two-terminal reliability at demand level d (M2TR_d) can be defined as the probability that the system capacity generated by multistate components is greater than or equal to a demand of d units. This paper presents a fully multistate-based algorithm that obtains the multistate equivalent of binary path sets, namely, Multistate Minimal Path Vectors (MMPVs), for the M2TR_d problem. The algorithm mimics natural organisms in the sense that a select number of arcs inherit information from other specific arcs contained in a special set called the “primary set.” The algorithm is tested and compared with published results in the literature. Two features of the algorithm make it relevant: (i) unlike other approaches, it does not depend on an a priori knowledge of the binary path sets to obtain the MMPVs; and (ii) the use of an information sharing approach and network reduction technique significantly reduce the number of vector analyses needed to obtain all the component levels that guarantee system success. Additionally, the complexities associated with the computation of reliability are discussed. A Monte Carlo simulation approach is used to obtain an accurate estimate of actual M2TR values based on MMPVs. Examples are used to validate the algorithm and the simulation procedure.     

Driver age, car mass and accident exposure— A synthesis of available data

The tendency of younger drivers to be more likely than older drivers to drive smaller cars has been an important consideration in a number of prior investigations of the relation between car size and traffic safety. The purpose of the present study is to quantify this effect on a firmer basis than hitherto by fitting data from seven independent sources to a unified general model. More specifically, when the exposure measures “per unit distance of travel” or “per registered car” are used in studies of car mass effects on traffic safety, the exposure information often does not contain the variable driver age. This work develops a general procedure for disaggregating such exposure data into three driver (or owner) age categories; A₁: 16–24; A₂: 25–34; and A₃: 35 years. Data from the seven sources are fined to the equation

f(i,m) = H_i[1 + G _i(m/900 − 1)]

where m is the ear mass in kg, and f(i,m) is the fraction of cars of mass m which are driven (owned) by persons in the A_i, (i = 1, 2, 3) age category. The form of this equation permits easy comparison of 900 and 1800 kg cars. Those particular masses that have been chosen for illustrative comparisons in earlier work. The seven sets of data are used to derive overall average values of the parameters H₁ and G₁. The data from all seven sources show consistent effects which are summarized in one analytical expression which is well suited for use in future studies of car size effects because it reflects a synthesis of much prior data and it permits sensitivity analyses to be performed conveniently.     

Crack tip damage development and crack growth resistance in particulate reinforced metal matrix composites

A study of crack tip damage development and crack growth resistance of aluminium 359/20% V_f silicon carbide and aluminium 6061/20% V_f Micral^Tm particulate reinforced metal matrix composites has been conducted. Observations of crack tip process zone development at the specimen surface have been compared with the results of fractographic examination of the centre of the specimen. Both materials were found to fracture by a process of void nucleation, growth and coalescence. Void nucleation was found to be by fracture or debonding of reinforcement particles, and/or fracture or debonding of secondary matrix particles. The preferred mode of void nucleation was found to vary depending on the constituents of the PR MMC and even the heat treatment state of the material. It was found that in these materials fractured particles identified on the fracture surface fractured during loading rather than being pre-cracked during fabrication. It was further found that observations of damage development from the specimen surface did not necessarily reflect the mechanisms prevailing in the specimen bulk. Under plane strain conditions, both materials were found to exhibit decreasing crack growth resistance as crack extension proceeded, due to the “anti-shielding” effect of damage accumulated in the process zone ahead of the crack tip. In thin specimens of the Comral-85 composite, however, dramatically improved toughness was obtained, and K_R curves have been obtained for such specimens. The method of measuring crack length was found to have a profound effect on the K_R curve; it was concluded that the K_R curve determined using the crack length measured at the specimen surface best reflected the true crack growth resistance of these materials.     

On the combined influences of Young''s modulus and stress ratio on the LEFM fatigue crack growth process: A new mechanistic approach

A new mechanistic approach (NMA) was used recently to examine the physical aspects of LEFM (long) fatigue crack growth (FCG) process in crack-ductile materials in stages I and II. In this paper, NMA is extended to examine both the physical and analytical aspects of the combined effects of Young's modulus, E and stress ratio, R, in the same stages of the same materials. It is shown that, (i) with submicroscopic cleavage or reversed shear mechanism operating in the pure form, E is the most influential intrinsic “material” property controlling FCG, (ii) E-dependence of da/dN is a natural consequence of near-crack-tip displacement control proposed previously, and (iii) the demonstrated similarity of FCG curves and the existence of characteristic “pivot points” on these curves for a “class of materials” results from E-influence which continues even at a higher R. A simple analytical model based on “strain intensity factor,” K₀, which contains E-influence implicitly and controls da/dN in all materials irrespective of class, is proposed. Model-predicted K₀-based theoretical values of threshold, “Idealised Master Growth Curves (IMGCs)” and mechanism transition point, all agreed excellently with experimental data for at least three classes of materials, i.e. steels, Al-alloys and Ti-alloys at extreme R-values of 0 and ≥ 0.6. The K₀-parameter concept is used here to raise the status of the analysis of the E-effect from a simple “normalisation” to that of direct data “representation”. Using NMA existing empirical relations are given some sound theoretical base. In addition to aiding in a clearer physical understanding of the FCG process, the unique IMGCs developed for different R-values are considered useful in quick, accurate and conservative life estimations, and performing failure analyses usually required in selection and design of materials.     

Biomimetic ion-channel sensors based on host-guest molecular recognition in Langmuir-Blodgett membrane assemblies

Biomimetic “ion-channel sensors” based on host-guest molecular recognition were constructed by incorporating several kinds of receptor molecules in Langmuir-Blodgett (LB) molecular assemblies deposited directly on glassy carbon electrodes. The receptors used were valinomycin, bis(crown ether)s, macrocyclic polyamine and cyclodextrin polyamine. The binding of charged stimulants (metal ions, inorganic and organic anions) to these receptors induced a marked increase (or decrease) in the ion permeability of the membranes, as detected by cyclic voltammetry using [Fe(CN)₆]^4- or [Ru(bpy)₃]²⁺ as marker ion. Such a mode of response, corresponding to model “channel opening (or closing)”, can be explained on the basis of the charge-charge interaction involving the stimulant, marker ion and lipid.     

Modifying the buckyball

Structural and electronic properties of carbon clusters, in particular the C₆₀ “buckyball” molecule as well as structurally and chemically modified fullerenes, are calculated using a combination of predictive ab initio techniques and parametrized total energy schemes. These calculations indicate that single- and multi-shell fullerenes are the most stable C_n isomers at T = 0 for n < 20. More open structures are favored by entropy at higher temperatures. Upon interaction with donor elements, C₆₀ molecules form stable M@C₆₀ endohedral complexes; analogous acceptor-based complexes are unstable. Solid C₆₀ reacts with alkali metals and forms a stable intercalation compound which shows superconducting behavior. The relatively high value of the critical temperature for superconductivity can be explained quantitatively within the Bardeen-Cooper-Schrieffer formalism.