Temperature dependence of electrical resistivity of deformed and undeformed V-rich V3Si single crystals

The electrical resistivity (T) of V-rich V₃Si single crystals (T _c-11.4 K) was measured from 4.2 to 300 K along the directions of [1 0 0] and [1 1 1] before and after plastic deformation at 1573 K. Anisotropy of (T) was observed although V₃Si has the cubic A15 structure. Plastic deformation does not affect the normal-state (T) behaviour but changes the normal-superconducting transition width T_c. At low temperatures (T _c<T 40 K), (T) varies approximately as T ⁿ where n-2.5 and this behaviour does not contradict the (0)- phase-diagram plot proposed by Gurvitch, where is the electron-phonon coupling constant and (0) is the residual resistivity.     

Superconducting state in M3C60: Strong vs. weak coupling

The superconducting state in the doped fullerenes is due to strong coupling (e.g.,2.1 for Rb₃C₆₀) to low-frequency intramolecular modes _L 250 cm^–1 (^21/2). The analysis is based on an equation describingT _c for any strength of the coupling and on recent isotope effect and NMR data.     

Spectral shape dependence in the very strong coupling regime of Eliashberg theory

The effect of ² F() shape dependence on several physical properties of superconductors is studied at various values of the strong coupling indexT _c/ _ln . Our results indicate that the degree of shape dependence of each property is sensitive to the value ofT _c/ _ln . Generally, for the region we examine, 0.25T _c/ _ln 1.3, the dependence on shape is found to be higher than in the conventional strong coupling regimeT _c/ _ln 0.2. However, with the exception of the mass enhancement parameter , the amount of shape dependence does not increase steadily withT _c/ _ln and there appears to be regions of maximum shape sensitivity.     

Anisotropic spin diffusion and multiple spin echoes in3He-4He solutions

We propose a ₁-t₁-₂ pulse-NMR experiment to detect the spin-diffusion anisotropy, =D-D, in degenerate spin-polarized³He-⁴He mixtures, where D and dare the transverse and longitudinal spin diffusion coefficients. In such an experiment the nonlinearity of the dynamics produces multiple spin echoes (MSE). At the ³He concentration x₃ 4% the spinrotation parameter vanishes (M 0), so that the nonlinearity of the equations of motion is entirely due to the anisotropy. In this situation, detection of MSE amounts to observation of D. For slight anisotropy, i.e. D/D 0.25, we use a perturbation scheme similiar to that developed by Einzel et al. (in that case, for small M and small demagnetizing field) to calculate the second and third echo heights. For larger anisotropy we numerically calculate the echo heights. We find that for D/D = 0.5 the heights are 2 % of the first echo, and should be detectable. The (₁, ₂) tip-angle dependence of the D echoes is different from that of the M and demagnetization echoes, and furthermore, they occur at right angles to these echoes (in spin space). Thus, even when small spin-rotation and demagnetization effects are present, the ₁-t₁-₂ experiment provides a sensitive means of detecting the anisotropy.     

A new formalism for time-dependent electromagnetic scattering from a bounded obstacle

In this paper a time-dependent three-dimensional electromagnetic scattering problem is considered. Let R ³ be the three-dimensional real Euclidean space filled with a medium of electric permittivity , magnetic permeability and zero electric conductivity. The quantities , are positive constants and there are no free charges in the space and the free current is taken to be zero. Let R ³ be a bounded simply connected obstacle with a locally Lipschitz boundary , that is assumed to have a nonnegative constant boundary electromagnetic impedance. The limit cases of perfectly conducting and perfectly insulating obstacles are studied. An incoming electromagnetic wave packet that hits is considered, and a method that solves the Maxwell equations to compute the corresponding electromagnetic field scattered by as a superposition of time harmonic electromagnetic waves is proposed. These time-harmonic electromagnetic waves are the solutions of exterior boundary-value problems for the vector Helmholtz equation with the divergence-free condition and they are computed with an `operator expansion' method that generalizes the method presented by L. Fatone et al.[J. Math. Phys. 40 (1999) 4859–4887]. The method proposed here is computationally very efficient. In fact, it is highly parallelizable with respect to time and space variables. Several numerical experiments obtained with a parallel implementation of the method are shown. The numerical results obtained are discussed from a numerical and a physical point of view. The quantitative character of the numerical experiments shown is established. The website: http://www.econ.unian.it/recchioni/w4/ contains some animations relative to the numerical experiments.     

Self-diffusion of Ti,Zr, and Hf in their hcp phases,and diffusion of Nb95 in hcp Zr

Preliminary values for the self-diffusion constants of -(hexagonal cp) Hf and new values for the self-diffusion constants of -(hcp) Zr are given. A new determination of the latter was considered necessary since existing values disagree widely and the experimental methods employed in their determination are not considered to be sound. Values obtained by the authors for the self-diffusion constants of -Ti are reviewed.The activation energies obtained are much smaller than those predicted by relationships based on physical properties of the elements and, within the experimental error, they have similar values to those corresponding to the -(body-centred cubic) phases. Frequency factors are too small to satisfy Zener's theory; when interpreted according to a vacancy model they give negative activation entropies, and the relationship D ₀()/D ₀() is approximately the same for the three elements.It is suggested that the same diffusion mechanism operates in both the - and -phases. If two mechanisms operate in the -phase, the low temperature one is the same as operates in the -phase.     

The preparation and characterization of ultrafine cobalt-iron oxides

Seven ultrafine samples (125 to 60 m²/g) of the cobalt-iron oxide series, Co _x Fe_3–x ,O₄, with 0x3, were prepared by co-precipitation of the metal hydroxides, followed by dehydration of the hydroxide at 100 C. X-ray and chemical analyses confirmed that true spinels were formed. The electrical conductivity and the activation energy for conduction of the powders were determined, and used to define the electronic structure of this series in conjunction with theoretical considerations based on crystal field theory.     

Effect of magnesium content on the stress exponent and effective stress in the steady state creep of Al-Mg alloys

The stress exponent of steady state creep,n, and the internal ( _i) and effective stresses ( _e) have been determined using the strain transient dip test for a series of polycrystalline Al-Mg alloys creep tested at 300° C and compared with previously published data. The internal or dislocation back stress, _i, varied with applied stress,, but was insensitive to magnesium content of the alloy, being represented by the empirical equation _i=1.084 ^1.802. Such an applied stress dependence of _i can be explained by using an equation for _i of the form _i (dislocation density)^1/2 and published values for the stress dependence of dislocation density. Values of the friction stress, _f, derived using the equation _e/=(1–c) (1– _f/), indicate that _f is not dependent on the magnesium content. A constant value of _f can best be rationalized by postulating that the creep dislocation structure is relatively insensitive to the magnesium content of the alloy.On leave from Engineering Materials Department, University of Windsor, Windsor, Ontario N9B 3P4, Canada.     

Vertical motion of a sphere in an electrically conducting,stratified, diffusive medium

Summary The vertical (upwards) flow of an incompressible, Newtonian, viscous, stratified, diffusive, electrically conducting fluid embedded with a uniform magnetic field that is applied in the vertical direction, past a non-conducting sphere is considered. Quasisteady approximation is made allowing for a time dependent buoyancy force. Method of matched asymptotic expansions is employed to obtain the drag exerted on the sphere, for small values of a stratification parameter such that 1,R _e ^1/3, ^–1/3,P _e ^2/3 andR _m =O(^2/3). The drag is computed for certain typical values of the magnetic interaction parameter and diffusivity parameter. The results reveal the fact that while the stratification and magnetic field have the enhancing effect over the drag, the effect of diffusivity is to decrease it.With 3 Figures     

Spin hydrodynamic equations with external disturbances and suitable Green's functions for superfluid3He-B. New onsager relations

The spin hydrodynamic equations for superfluid³He-B have been obtained for the case of external, time-dependent fields. On the basis of a microscopic approach, expressions are found for additional terms in equations containing these fields. Considering the linear response of the system to the switching on of external fields, formulas are found for suitable Green's functions (magnetization-magnetization, rotation-rotation, magnetization-rotation, rotation-magnetization). The rotation-rotation Green's function has the 1/q ² singularity characteristic of superfluid systems. Connections between Green's functions lead to relations among kinetic coefficients v, ₁, and ₂. It is also shown that there is a conserved quantityQ ^(B) = div v _s ^(B) that describes sources or magnetic type charges (monopoles) of the superfluid velocity v _s ^(B) . Comparison with the phenomenological approach suggests thatQ ^(B) is proportional to a pseudoscalar giving the projection of the spin density onto the vector describing the axis of rotation.     

Phase Diagrams at Different Fillings of the Effective Extended Hubbard–Holstein Hamiltonian for a Four-Site Ring of Variable Length

The effective fermionic Hamiltonian derived from the extended Hubbard–Holstein model by a sequence of generalized displacement and squeezing transformations, contains new, long-range, intersite charge interactions. By exact diagonalization on a four-site ring with equally spaced sites, followed by variational optimization of the energy, we obtain the phase diagrams for 2, 3, and 4 electrons by using interaction parameters expressed as functions of the interatomic distance. Depending on the filling, the new charge interaction can modify the phase diagram appreciably.     

Bifurcation of crack pattern in arrays of two-dimensional cracks

Theoretical calculations based on simple arrays of two-dimensional cracks demonstrate that bifurcation of crack growth patterns may exist. The approximation used involves the dipole asymptotic or pseudo-traction method to estimate the local stress intensity factor. This leads to a crack interaction parametrized by the crack length/spacing ratio =a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (bifurcation) if is larger than a critical value _cr. However, no such bifurcation is found for a collinear crack array under tension. For parallel and edge crack arrays, respectively, the value of _cr decreases monotonically from (2/9)^1/2 and (2/15.096)^1/2 for arrays of 2 cracks, to (2/3)^1/2/ and (2/5.032)^1/2/ for infinite arrays of cracks. The critical parameter _cr is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain _cr for infinite crack arrays. For infinite parallel crack arrays under uniaxial compression, a simple shear-induced tensile crack model is formulated and compared to the modified Griffith theory. Based upon the model, _cr can be evaluated numerically depending on (the frictional coefficient) and c ₀/a (c ₀ and a are the sizes of the shear crack and tensile crack, respectively). As an iterative method is used, no closed form solution is presented. However, the numerical calculations do indicate that _cr decreases with the increase of both and c ₀/a.     

Thermal stresses in a thin circular disc of orthotropic material due to an instantaneous point heat source

Summary In this paper, we have analysed the transient plane thermal stress problem of a circular disc of orthotropic material with instantaneous point heat source. The variation of with time along different radius vectors is exhibited graphically and compared with that of the isotropic case.

---

Wärmespannungen in einer dünnen Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle

Zusammenfassung In dieser Arbeit wurde das instationäre ebene Wärmespannungsproblem einer Kreisscheibe aus orthotropem Material zufolge einer punktförmigen instantanen Wärmequelle untersucht. Die Veränderung von über die Zeit für verschiedene Radien ist graphisch dargestellt und wird mit dem isotropen Fall verglichen.

---

Nomenclature r, polar coordinates - T temperature rise - ² ratio of conductivities - ² thermal diffusivity in -direction - J _n Bessel function ofn-th order - t time - p introduced in equation (2) - h heat transfer coefficient - a radius of circular disc - f(r, ) temperature distribution at initial state - r ₀, ₀ a point on the disc - T ₀ strength of point heat source - Dirac delta function - F stress function in two dimensions - ₁, ₂ coefficient of thermal expansion - a ₁₁,a ₁₂,a ₂₂,a ₆₆ elastic constants With 9 Figures     

Analysis of strain localization in strain-softening hyperelastic materials,using assumed stress hybrid elements

Newly developed assumed stress finite elements, based on a mixed variational principle which includes unsymmetric stress, rotation (drilling degrees of freedom), pressure, and displacement as variables, are presented. The elements are capable of handling geometrically nonlinear as well as materially nonlinear two dimensional problems, with and without volume constraints. As an application of the elements, strain localization problems are investigated in incompressible materials which have strain softening elastic constitutive relations. It is found that the arclength method, in conjunction with the Newton Raphson procedure, plays a crucial role in dealing with problems of this kind to pass through the limit load and bifurcation points in the solution paths. The numerical examples demonstrate that the present numerical procedures capture the formation of shear bands successfully and the results are in good agreement with analytical solutions.List of Symbols u displacement - R rotation - U right stretch tensor - r^* Biot stress tensor - t first Piola Kirchhoff stress tensor - Cauchy stress tensor - I identity tensor - F deformation gradient I+(u)^T - ab a _ib_jg ⁱ g ^j =dyad - a·b a _ibⁱ=dot product - A·b A _ijb^j g ⁱ - A·B A _ikB _inf.j ^supk. g ⁱ g ^j - A:B A _ijB^ij - v velocityu - W spin tensorR - D rate of stretch r - r^* UL rate of r^* - t UL rate of t - _n Kronecker's delta - - J det F=det{I+(u)^T} - symm (A) 1/2(A+A ^T ) - skew (A) 1/2(A-A ^T ) - trace (A) A _inf.i ^supi. This research is supported by the Office of Naval Research. The first author wishes to express his appreciation to Dr. H. Murakawa, Dr. E. F. Punch, Mr. A. Cazzani, and Dr. H. Okada for fruitful discussions on the subject     

On a simple wave approximation of a set of linear dispersive wave equations

Summary The validity of an approximation ₀ of one of the solutions of a set of two linear coupled dispersive wave equations has been discussed. ₀ is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as . It is shown that for square integrable solutions having a spectral range not exceeding [–, ] the approximation is useful if ^{5 2}t«1 in the sense that –₀(t)« (t)(L ₂ -norm). is a measure for the dispersion. The approximation fails in that sense ast . Some remarks to a similar nonlinear problem are made.     

Isochoric Heat Capacity of Heavy Water at Subcritical and Supercritical Conditions

The heat capacity of heavy water was measured in the temperature range from 294 to 746 K and at densities between 52 and 1105 kg·m^–3 using a high-temperature, high-pressure adiabatic calorimeter. The measurements were performed at 14 liquid and 9 vapor densities between 52 and 1105 kg·m^–3. Uncertainties of the measurements are estimated to be within 3% for vapor isochores and 1.5% for the liquid isochores. In the region of the immediate vicinity of the critical point (0.97T/T _c1.03 and 0.75/_c1.25), the uncertainty is 4.5%. The original C _V data were corrected and converted to the new ITS-90 temperature scale. A parametric crossover equation of state was used to represent the isochoric heat capacity measurements of heavy water in the extended critical region, 0.8T/T _c1.5 and 0.35/_c1.65. The liquid and vapor one- and two-phase isochoric heat capacities, temperatures, and saturation densities were extracted from experimental data for each measured isochore. Most of the experimental data are compared with the Hill equation of state, and the overall statistics of deviations between experimental data and the equation of state are given.     

Compressibility measurements of β- and β″ -alumina

The compressibilities of the a- and c-axes for sodium - and -aluminas were determined up to 10 GPa from the pressure dependence of powder X-ray diffraction measured at room temperature using synchrotron radiation as an X-ray source. Powders of sodium - and -aluminas which were prepared from grinding synthesized single crystals were used as the specimens for X-ray diffraction. The compressibilities of - and -aluminas are 1.5 ± 0.2 ×10^–12 and 1.7 ± 0.2 × 10^–12 Pa^–1 for the a-axis and 2.9 ± 0.2x10^–12 and 1.6 ± 0.2 ×10^–12 Pa^–1 for the c-axis, respectively. For the c-axis, the compressibility of -alumina is larger than that of -alumina. This experimental fact is explained by the different stacking of oxygen layers and the different content in sodium ion between - and -aluminas.     

Heat conduction in a multilayer composite wedge

A new method for analytically solving a problem of steady-state heat conduction for multilayer composite wedge-shaped bodies is suggested based on a generalization of the integral Mellin transform.Notation T temperature - _rr, thermal conductivity coefficients - thickness of composite material layers (1) - N₁(), N ₂ ⁽¹⁾ (), N ₂ ⁽²⁾ () auxiliary local functions from the rapid variable =r/ - m(r, p) auxiliary function entering the core of the generalized integral Mellin transform - ₀ half of the wedge aperture angle Moscow Institute of Chemical Engineering. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 64, No. 4, pp. 487–491, April, 1993.     

Microstructure refinement with forced convection in aluminium and superalloys

The cooling and average local solidification times were determined for slow solidifiation of Al-4.4 wt% Cu alloy under natural convection and under electromagnetically forced axisymmetric rotation during liquid cooling and solidification in graphite moulds. Cooling rates were measured within situ thermocouples. The conditions needed to stabilize the radial temperature gradient with rotation were established. The microstructure size decreased with increasing rotation, as did the local solidification times. The average grain and dendrite size without imposed rotation is coarser near the mould wall compared with the centre of the casting. This trend is reversed with imposed rotation. Rotation also led to a smaller spread of grain and dendrite size at any chosen height of the casting. These results are discussed in relation to existing theories, and several reasons for an improved heat transfer coefficient with rotation are presented. Forced convective solidification was then carried out for various shapes of integral investment cast Nimonic-90 alloy solidifying under modified conditions that prevented columnar grain formation. Similar results to those recorded for the aluminium case were obtained and are presented here. The major conclusion is that observations indicating a reduction of microstructure spacing during forced convection should also consider improved heat extraction at the mould-metal interface.List of symbols Gr Grashof number =gTZ ^{3 3}/ ³ - g _r acceleration in radial direction - g acceleration in direction - g _z acceleration inZ direction (gravity) - h heat transfer coefficient - k _l thermal conductivity of liquid - Nu _z Nusselt number =hZ/k _l - Pr Prandtl number =/ - Ra Rayleigh numberGr Pr - R radius of mould - Re _r Reynolds number =V ₀ R/ - T temperature - T temperature difference in radial direction - Ta Taylor number = ²4H ⁴ W ²/ ² - V velocity - W r.p.m. - thermal diffusivity - coefficient of volume expansion - viscosity - density Mr G. S. Reddy is also a post graduate student registered at the Banaras Hindu University, Varanasi, India.     

Effects of alloying in the dilute limit on the quantum states of electrons in magnesium

The electron quantum interference phenomenon was used to determine the effects of substitutional alloying upon the quantum-state lifetime and band gapsE _g at the Fermi energy in single crystals of pure Mg. Vapor-grown alloys containing either Zn or Cd in concentrationsC0.3–15 ppm were studied. The magnetic field dependence of the interference oscillation amplitudes for these samples indicates reductions in and significant increases inE _g relative to pure Mg (impurity concentration 10^–8). Within experimental accuracy the observed quantum-state lifetime satisfies the relation ^–1=C, with 2.7×10¹⁰ sec^–1 per ppm of Cd and 2×10¹¹ sec^–1 per ppm of Zn. The band gap corresponding to Bragg reflection from the (0001) plane of the hcp structure (which in pure Mg arises solely from spin-orbit coupling) was found to increase by more than a factor of two upon the addition of only 10 ppm Cd to Mg. These results are discussed within the framework of the pseudopotential theory of alloying. It is shown that there are discrepancies of more than three orders of magnitude between the experimental and theoretical values forE _g and of about one order of magnitude for in these dilute-limit alloys.Work supported by the National Science Foundation.Submitted to the Department of Physics, the University of Chicago in partial fulfillment of the requirements for the degree of Doctor of Philosophy.Fannie and John Hertz Foundation Fellow.