ALE-based 3D FE simulation of electromagnetic forming

Electromagnetic forming is a contact-free high-speed forming process. The deformation of the work piece is driven by the Lorentz force which results from the interaction of a pulsed magnetic field with eddy currents induced in the work piece by the field itself. The purpose of this work is to present a fully-coupled three-dimensional simulation of this process. For the mechanical structure, a thermoelastic, viscoplastic, electromagnetic material model is relevant, which is incorporated in a large-deformation dynamic formulation. The electromagnetic fields are governed by Maxwell's equations under quasistatic conditions. To consider their reduced regularity at material interfaces Nédélec elements are applied. Coupling takes the form of the Lorentz force, the electromotive intensity and the current geometry of the work piece. A staggered solution scheme based on a Lagrangian mesh for the work piece and an ALE formulation for the electromagnetic field is employed. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two forms of aluminium phosphate tridymite from X‐ray powder data

Monoclinic and triclinic (pseudo‐orthorhombic) AlPO₄ tridymites have been refined from X‐ray powder diffraction data using the silica analogues as starting models. The framework structures of both forms of tridymite are made up of six‐membered rings of tetrahedra which differ in the distortion patterns of the ring shapes. Ordered occupation of alternate tetrahedra by Al and P leads to a doubling of the a lattice parameter for monoclinic AlPO₄ tridymite (space group Pc) and loss of the C‐centring with respect to the isotypic silica tridymite (space group Cc). Triclinic AlPO₄ tridymite was refined in the same space group (F1) as the SiO₂ analogue.     

Physical vapor transport and crystal growth of GeSexTe1−x solid solutions

Physical vapor transport studies of GeSe_xTe_1–x (x = 0.1, 0.2, 0.3, and 0.4) solid solutions demonstrated, that individual, large single crystals of these materials can be grown in closed ampoules. A compositional analysis of the grown crystals revealed, that the mass transport (crystal growth) process under steady-state conditions is pseudo-congruent and controlled by diffusion processes in the source material. From these experiments, the degree of nonstoichiometry (Ge-vacancy concentrations) of GeSe_xTe_1–x single crystals could be estimated. The effects of the cubic to rhombohedral phase transformation during cooling on the microstructure and morphology of the grown mixed crystals are observed. This work provides the basis for subsequent defect studies and electrical measurements on these crystals.     

The direct determination of the vacancy concentration and P-T phase diagram of Hgin0.8Zn0.2Te by dynamic mass-loss measurements

A modified mass-loss measurement technique is employed, for the first time, for the direct, in-situ determination of the metal vacancy formation in (Hg_0.8Zn_0.2)_1-yTe_y,(s). The metal vacancy concentrations are determined between 350 and 650° C for four different compositions(y) within the homogeneity region and range from 1.7 to 6.6 × 10¹⁹ cm^-3. The enthalpy of formation of a singly-ionized metal vacancy is derived to be between 0.32 and 0.72 eV depending upon the deviation from stoichiometry (compositiony). Com-pared to the recent data on HgTe(s), these experimental results show a slight but sig-nificant increase in the enthalpy of vacancy formation from HgTe to Hg_0.8Zn_0.2Te. These data provide the first, direct experimental evidence, in terms of vacancy formation en-ergy, supporting theoretical predictions of the bond strengthening effect of Zn for the latter alloy system. Based on the simultaneously determined equilibrium Hg partial pressures within the homogeneity range, the vacancy concentration-partial pressure iso-therms are constructed. The Hg partial pressures are also measured along the three-phase boundaries of the solid solutions, and these are in close agreement with published data obtained by optical absorption measurements. A considerable part of the P-T phase diagram is, thus, established in this work.     

A thermodynamic model of The Hg0.8 Cd0.2 Te-Iodine Transport System. I. Te-saturated source material

Based on the formation of an ideal solid solution between CdTe and HgTe, the thermodynamic analysis of the complex Hg_1?xCd_xTe-iodine chemical vapor transport system could be somewhat simplified because the source material composition was at the Te-rich boundary of the homogeneity range of Hg_0·8Cd_0·2Te. This led to the development of a first order approximation model for the prediction of diffusion limited mass transport rates. The agreement between computed and experimental (vertical, stabilizing conditions) mass transport rates is quite satisfactory.     

The Generalized Trotter Operator and Weak Convergence Of Dependent Random Variables in Different Probability Metrics

The Trotter operator-theoretic method for establishing weak convergence of sums of real-valued random variables X _{i i∈N} on a probability space (Ω,A,P) is extended to the situation that the X_i are dependent. For this goal, the generalized Trotter-operator is defined for functions f∈C_b and a sub- σ algebra G ? A by V_X¦G f (y) ? ∫_Rf(x+y) dP_X¦G(x,w). General results concerning the weak convergence of dependent random variables (r.vs.) with rates are presented. Further, the distance V between the distributions P,Q of two random variables X,Y with respect to a function f and a sub-σ algebra G, namely the Trotter-distance V(P,Q;f), defined via the generalized Trotter-operator by V(P,Q;f) = sup_y¦∫_Rf(x+y) d(P?q)(x)¦, is compared with other well-known probability-metrics, which metrize weak convergence, such as the Zolotarev-metric ξ, the Gudynas-metric η, the Levy-metric L or the Prohorov-metric ?. Lastly, the Trotter-distance with rates is shown to be equivalent to weak convergence with rates.     

Defects in CdTe single crystals grown by very fast vapor growth technique

Single crystals of CdTe were obtained by the very fast vapor growth technique. The four major defects, namely, multi-grains, lamellar, lateral, and micro-twins, which are fatal to the single crystallinity, were eliminated or limited by increasing the growth stability. This investigation indicates that the latent heat under high growth rate conditions should not be neglected. A model is developed to explain the effects of latent heat on the growth stability at the interface. A relationship between crystal morphologies and growth conditions was established. It strongly suggests that the above defects are growth stability related. The origin of twinning, dominated by growth stability, is discussed in this paper.     

Characteristics of island growth of Hg1−xCdx Te on (100) CdTe substrates by chemical vapor transport

The characteristics of island growth of Hg_1−xCd_xTe (MCT) by chemical vapor transport on (100) CdTe substrates have been studied, for the first time, by optical microscopy, by infrared transmission spectroscopy, and by chemical etching. Nonuniformities of the growth thickness, of the growth rate, and of the composition of islands are observed. Based on the experimental results, the origin and the inhibition of island growth of MCT on (100) CdTe substrates are discussed.