Optical transitions near the band edge in bulk CuInxGa1−xSe2 from ellipsometric measurements

From the analysis of the variation of optical absorption coefficient with incident photon energy between 0.8 and 2.6 eV, obtained from ellipsometric data, the energy E_G of the fundamental absorption edge and E_G′ of the forbidden direct transition for CuIn_xGa_1−xSe₂ alloys are estimated. The change in E_G and the spin-orbit splitting Δ_SO=E_G′−E_G with the composition x can be represented by parabolic expression of the form E_G(x)=E_G(0)+ax+bx² and Δ_SO(x)=Δ_SO(0)+a′x+b′x², respectively. b and b′ are called “bowing parameters”. Theoretical fit gives a=0.875 eV, b=0.198 eV, a′=0.341 eV and b′=−0.431 eV. The positive sign of b and negative sign of b′ are in agreement with the theoretical prediction of Wei and Zunger [Phys. Rev. B 39 (1989) 6279].     

The scaling of impact phenomena

A basis for scaling laws for impact phenomena is the approximation of the actual problem with a point-source problem. Point-source solutions are characterized by a single scalar coupling-parameter measure aU^μδυ of the radius a, velocity U and mass density δ of the impactor. Point-source solutions that are known to exist are discussed. The implications to scaling are developed. Recent numerical code calculations that were designed to investigate the scaling and the application of the coupling parameter are presented. Finally, a summary of some recent applications of the theory is given.     

Nonsteady penetration of longs rods into semi-infinite targets

This paper describes a new one-dimensional theory of nonsteady penetration of long rods into semi-infinite targets. The target is viewed as a “finite mass” that resides within the semi-infinite target space. Thus, an equation of motion for the target was constructed so that together with erosion and penetrator deceleration equations, expressions for penetration rates and depths were obtained. Forces acting on the target and penetrator are defined in terms of only ordinary strength levels usually associated with dynamic properties or work-hardened material states. Also, the concept of critical impact velocity was used to establish the onset of penetration in this formulation. This penetration equation corresponds in exact form to hydrodynamic theory in the limits of small strengths and/or high impact velocity. Results for penetration rates agree well with hydrocode calculations, and predicted penetrations agree with experimental data over an impact velocity range of 0–5,000 m/s.     

Affect of shock-induced phase transformations on dynamic strength of titanium alloys

A series of complex alloyed (+β) VT-16 Titanium alloy targets were subjected to shock loading under uniaxial strain conditions within impact velocity range of 276–600 m/s. The tests reveal a presence of forward (→ω) and (β→ω) phase transitions at the load front and reverse (ω→β ) transition at the release front of compressive pulse. Duration of (β→ω) and (ω → β ) transitions is approximately 0.5 μs. When spallation happens after reverse (ω →β) phase transition, the spall-strength of alloy increases by 25%. Oscillating regime of that transformation proves to widen the impact velocity range where the spall-strength is maximum.     

Role of plastic work in fatigue crack propagation in metals

The plastic work required for a unit area of fatigue crack propagation U was measured by cementing tiny foil strain gages ahead of propagating fatigue cracks and recording the stress-strain curves as the crack approached. Measurements of U and plastic zone size in aluminum alloys 2024-T4, 2219-T861, 2219 overaged, and A1-6.3 wt% Cu-T4, and a binary Ni-base alloy with 7.2 wt% A1 are herein reported. The results are discussed along with previously reported measurements of U in three steels and 7050 aluminum alloy. When U is compared to the fatigue crack propagation rate at constant ΔK along with strength and modulus, the conclusion is drawn that U is one of the parameters which determines the rate of fatigue crack propagation. The relation of U to microstructure is also discussed. “Homogeneous” plastic deformation in the plastic zone ahead of the crack seems desirable.     

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.     

Secondary bifurcations in systems with all-to-all coupling. Part II.

In a recent paper Dias and Stewart studied the existence, branching geometry, and stability of secondary branches of equilibria in all-to-all coupled systems of differential equations, that is, equations that are equivariant under the permutation action of the symmetric group S_N. They consider the most general cubic order system of this type. Primary branches in such systems correspond to partitions of N into two parts p, q with p + q = N. Secondary branches correspond to partitions of N into three parts a, b, c with a + b + c = N. They prove that except in the case a = b = c secondary branches exist and are (generically) globally unstable in the cubic order system. In this work they realized that the cubic order system is too degenerate to provide secondary branches if a = b = c. In this paper we consider a general system of ordinary differential equations commuting with the permutation action of the symmetric group S_3n on R³ⁿ. Using singularity theory results, we find sufficient conditions on the coefficients of the fifth order truncation of the general smooth S_3n-equivariant vector field for the existence of a secondary branch of equilibria near the origin with S_n × S_n × S_n symmetry of such system. Moreover, we prove that under such conditions the solutions are (generically) globally unstable except in the cases where two tertiary bifurcations occur along the secondary branch. In these cases, the instability result holds only for the equilibria near the secondary bifurcation points. We show an example where stability between tertiary bifurcation points on the secondary branch occurs.     

Ion formation by high velocity impacts on porous metal targets

In impact ionization studies the target normally consists of a metal surface of compact solid density. In the present experiments, we investigate the use of a layer of a highly porous structure of nanometre-sized grains, sometimes also called “metal black”, as an alternative target. In our comparative experiments, spherical iron particles (0.1<d_p<1.5 μm) were shot with velocities 2–30 km/s onto both a compact solid silver plate and a silver metal black layer of about 7 μm thickness (grain size 20–40 nm, mean density ≈1 g/cm³), deposited on a compact solid gold plate. Impact generated ions were analysed by means of time-of-flight mass spectrometry. The results reveal important advantages of the porous black layer, such as better mass resolution and a larger amount of ions from the impacting particle. Therefore metal blacks may be very suitable targets for the purposes of identification and characterisation of the impacting particle's composition. An attempt is made to give a physical explanation of the results in the frame of existing empirical ionization models. The study is part of a programme to improve devices for in-situ analysis of fast moving cosmic dust particles.     

Dissociation process of CH4/H2 gas mixture during EACVD

The dissociation process of CH₄/H₂ gas mixture during EACVD has been investigated using Monte Carlo simulation for the first time. The electron velocity distribution and H₂ dissociation were obtained over a wide range: 100<E/N<2000 Td. The variation of CH₄ dissociation with CH₄ concentration in the filling gas has been simulated. The electron velocity profile is asymmetric for the component parallel to the field. Most electrons possess non-zero velocity parallel to the substrate. The number of atomic H is a function of E/N. There are two peaks at E/N=177 Td and 460 Td. The appropriate E/N is suggested to be 500–800 Td for low temperature deposition. The main diamond growth precursor is proposed to be CH₃ and CH₃⁺.     

The penetration of rigid long rods – revisited

The penetration process of rigid long rods with different nose shapes (ogive, spherical, conical and flat) is analyzed through a series of 2D numerical simulations. Aluminum and steel targets with different strengths (and large dimensions) are used to follow the deceleration process of these rods from impact, at different velocities, to the final penetration point. We find that for low impact velocities the deceleration of these rods is practicably constant, depending only on the strength of the target and the nose shape of the rod. Above a threshold (critical) impact velocity rod deceleration becomes velocity dependent due to the inertial response of the target. These critical velocities depend on the strength of the target and the nose shape of the rod. These observations led us to propose a simple penetration formula which accounts very well for penetration depths data for rigid steel rods with different nose shapes, impacting various aluminum targets at velocities up to about 1.5 km/s. For higher impact velocities, where the dynamic (inertial) contribution to the target resistance is important, we find good agreement between our model predictions and the simulation results for final penetration depths.     

Experiments on the study of effect of microparticles anomalistic penetration into solid bodies

At certain conditions interaction between high velocity (up to 3 km/s) flows of microparticles with dimensions 20–70 μm and solid bodies could result in their super deep penetration (SDP) into those bodies. For SDP-effect to be studied a number of experiments were carried out. The X-ray analysis of microparticles acceleration has shown the advantage of acceleration of microparticles in mixture with the extender (porofor) because it makes it possible to regulate the flow density, its velocity and impact duration by means of the extender concentration variation. Experiments have been performed on the impact of microparticle flows with velocities in the range 1–2.6 km/s on copper and iron substrates. Results of metallographic investigations of cross-sectional and lengthwise grinds of substrates indicate that some tungsten particles penetrate into a target. The diameter of channels in the substrate material, which are formed due to particles penetration, is in the range 2–15 μm.     

Hypervelocity impact of rod projectiles with L/D from 1 to 32

Beside a short remark on the “hydrodynamic theory of rod projectiles”, the paper deals with the terminal ballistic behaviour of cylindrical projectiles against semi-infinite targets. Experimental data of EMI, completed by results of some other authors, are presented. Crater parameters like depth, diameter and volume and their dependence on projectile velocity (up to 5000 m/s), projectile and target material properties, as well as L/D-ratios (1–32), will be discussed. Mainly the projectile materials steel and tungsten sinter-alloys are considered. Target materials are mild steel and high strength steel, an Al-alloy and a tungsten sinter-alloy. The results show that the influence of material density on the crater dimensions is considerably greater than the influence of strength. The L/D ratio determines the velocity dependence of crater depth, diameter and volume. At high velocities in the hydrodynamic regime, the crater depth of short cylinders (L/D 1) is approximately proportional to v_p^2/3 (V_p=projectile velocity). With increasing L/D-ratio, the slope of the penetration curves decreases and converges for rods (L/D 1) versus a saturation, i. e. becomes nearly independent on v_p. A consequence of this saturation is the existence of a so-called “tangent velocity”, above which an optimal increase of efficiency is only realized by increasing the projectile mass and not the velocity. Furthermore, ballistic limits of real targets like single plates and symmetric double plates meteorite bumper shield) are taken into account. The expected better performance of “segmented rods” is also discussed.     

Mechanical behaviour of a two-phase material from the behaviour of its components: Interface modelling by finite element method

In this paper, the principle of a solution for “thermal” connection between two solids is analyzed. We shows results given by the solution applied to the mechanical behaviour of a γ/γ′ two-phase material and to “artificial” structures obtained from modern techniques for epitaxial deposit. It appears that the use of a true or fictitious thermal loading constitutes a simple “connection” procedure, but is particularly coherent with the mechanics of two-phase crystalline materials with different lattice parameters. It would be interesting to apply the model to real structures, with misfit and interfacial dislocations.     

An improvement to the space resolution of charged tracks

A simple tracking method is to look for the U, X and V triple coincidences in a wire chamber, but the space resolution is in general not satisfactory. In this paper, we consider the use of space correction for the inclined planes in a chamber. The resolution can be much improved for both the proportional chamber and the drift chamber. For proportional chambers, the combination of this method and the wire-spacing “drift distance” technique, further improved the resolution.     

Effect of yield stress and specimen size on the position of fracture toughness peak (FTP) in Ji-a/W curves

Early work showed that there was a fracture toughness peak (FTP) as the fracture toughness changed with crack length/specimen width (a/W). It could be thought of as a “safe crack” for the cracks whose length is smaller than that where the FTP is located. In the present paper, it is indicated that the crack length of FTP isJ_i-a/Wcurves decreases with increasing yield stress of material and specimen size and decreasing test temperature. The reason for the fracture toughness being insensitive to the (a/W) for the ultra-high strength and brittle material is explained.     

Hypervelocity impact testing of micrometeorite capture cells in conjunction with a PVDF thin-film velocity/trajectory sensor and a simple plasma velocity detector

Five different small particle capture cell designs were evaluated for their ability to capture fragments and residue from 10–200 μm diameter glass projectiles and oblong olivine crystals impacting at 1–15 km/s in sufficient quantity for chemical and isotopic analyses. Aluminum multi-foils (0.1–100 μm thick with ≈10, 000 and 1800 μm spacing), foil covered germanium crystals, and 0.50 and 0.120 g/cm³ Aerogels, were positioned behind either multi-film (1.4–6.0 μm thick) polyvinylidene fluoride (PVDF) velocity/trajectory sensor devices of a simple wire-grid plasma velocity detector. All capture cells collected significant amounts of impactor debris behind the PVDF sensors from nominal 100 μm diameter glass projectiles and olivine crystals which struck the sensor at velocities up to 6.4 km/s. At velocities >8 km/s little or no debris penetrated the second PVDF film. Results were incolsive for velocities between 6.5 and 8 km/s. Plasma detector results showed identifiable impactor residue on Al foils for velocities up to 8.7 km/s and impact tracks with apparent debris imbedded in the Aerogels for velocities up to 12.7 km/s. Maximum foil penetration of glass spheres and olivine crystals were the same, but more particulate debris was associated with olivine crystal ipacts versus glass impacts. Foil spacing beyond one particle diameter had no effect on total penetration. Aerogels are identified as a capture cell media that warrants further investigation. The Al multi-foil capture cell with 100 μm net spacers is identified as the most effective of the other designs and offers the advantages of compact structure, low secondary ejecta from impacts, and easy recovery of impactor debris for analysis.     

Impact and penetration by L/D ≤ 1 projectiles

Calculations of steel target penetration by L/D ≤ 1 tungsten and tungsten alloy projectiles have been extended to L/D = 1/32 over the velocity range 1.5 to 5 km/s. The ratio of crater to projectile diameter tends to 1 as L/D decreases over this entire velocity range. For impact velocities of 1.5 and 3 km/s, penetration depth normalized by projectile length, P/L, increases with decreasing projectile L/D up to a maximum value and then decreases for still lower L/D. Experiments at impact velocities of 2 and 3 km/s confirm these results. For 5 km/s impact velocity, the calculations show P/L increasing with decreasing projectile L/D over the entire range 1/32 ≤ L/D ≤ 1. The projectile L/D for which the maximum P/L occurs appears to depend on the impact velocity. P/L generally scales with impact velocity as P/L v^f(L/D) where f(L/D) ranges from 0 for a long rod to, we believe, 2 in the limit as projectile L/D approaches zero. The calculations show for 1/8 ≤ L/D ≤ 1/2, P/L v^0.9; for L/D = 1/16, P/L v^1.5; and for L/D = 1/32, the new results give P/L v^1.9.     

Theoretical considerations on the penetration of powdered metal jets

This paper explores some of the theoretical issues encountered when interpreting the penetration behavior of an oilwell perforating charge, whose jet forms from an unsintered powdered metal (PM) liner. Appropriate treatments of the jet's porous compressible nature fill the gap between classical “continuous” and “fully particulated” jet penetration models. Within certain constraints, increasing a penetrator's length (even if by distension) increases its hydrodynamic penetration depth, while reducing its impact pressure; and a porous penetrator penetrates deeper than a non-porous penetrator of the same density, length, and velocity. Dynamic target pressure considerations lead to the conclusion that highly distended, low-velocity, PM jets should penetrate moderate-strength geologic targets effectively. After demonstrating that initial transient shock pressures may be much higher than steady-state penetration pressures, we suggest that initial penetration rates may be higher than the steady-state rates. This, in conjunction with the well-known “residual penetration” phenomenon, indicates that a non-continuous jet's penetration may be strongly influenced by transient effects.     

Existence of periodic solutions of the equations of incompressible micropolar fluid flow

The equations of incompressible micropolar fluid flow are a coupled system of vector differential equations involving the two basic vectors, viz. the velocity and the microrotation of the fluid elements. Let D = D (t) be a bounded region in space, and let a flow velocity and a microrotation be prescribed at each point of the boundary of D(t). Assume that D(t) as well as the assigned velocity and microrotation vectors depend periodically on the time t and that the condition (2μ+k)j−4a 0 is satisfied (equation (25) in the text). Further assumptions are that (i) to every continuous initial distribution of the flow fields over D, there corresponds a solution of the field equations for all time t 0 satisfying the prescribed boundary conditions; (ii) there is one solution for which the Reynolds numbers Re, Rm satisfy the condition Re² + Rm² < 80 and this solution is equicontinuous in for all t. Then there exists a unique, stable, periodic solution of the micropolar flow equations in D(t) taking the prescribed values on the boundary. The proof of the theorem rests on a formula describing the rate of decay of the kinetic energy of the difference of two micropolar flows in the domain subject to the same boundary conditions.