Microstructure of a rapidly solidified 65Al-20Cu-15Fe (at. %) alloy

The microstructure of rapidly solidified 65Al-20Cu-15Fe (at. %) powders was investigated by analytical transmission electron microscopy. It was found that segregation in the powder particle occurred during solidification. The major phase present in the powder particles was the icosahedral quasicrystalline l-phase, which was determined to have space group . Two other crystalline phases, -AlCu₃ and -Al₁₃Fe₄, coexisted with the l-phase. The l-phase was revealed by convergent beam electron diffraction to have three-dimensional quasiperiodicity ( = 1.618) which is different from quasicrystals in the other systems. The compositions of the three phases have been analysed by energy dispersive X-ray analysis. The l-phase in this system could be approximately described as Al₅CuFe. The composition of the -Al₁₃Fe₄ was very close to the equilibrium condition while -AlCu₃ was far from stoichiometry. An orientation relationship between -AlCu₃ and -Al₁₃Fe₄ was found as follows: [110][010] [111][001]     

Effect of resonant impurity scattering on collective mode peaks in the ultrasound attenuation of heavy fermion superconductors

We have calculated the attenuation of longitudinal ultrasound due to real order parameter fluctuations in impure polar and planarp-wave superconductors. The quasiparticle self-energy and the corresponding vertex corrections have been included in thet-matrix approximation for arbitrary scattering rate =1/2_N and all scattering phase shifts _N (0 _N/2). We obtain sound attenuation peaks belowT _c whose heights, positions, and shapes depend on ₀ (sound frequency), (₀), _N, and (coupling strength due to particle-hole asymmetry). The peaks become much more distinct and sharper for _N =/2 (resonant scattering by impurities) than for _N=0 (Born approximation). By choosing , _N, and suitably, qualitative agreement between calculated and observed peaks in UBe₁₃ and UPt₃ can be achieved.     

Microstructure and mechanical properties of metastable lath martensite wires in the Fe-Ni-Cr-Al-C system produced by melt spinning in rotating water

Metastable lath martensite ( _L ) phase wires with high strengths have been produced in the Fe-Ni-Cr-Al-C alloy system by melt spinning in rotating water. These wires have a circular cross section and a white lustre and the wire diameter is in the range of 100 to 140m. The width and length of each lath in the _L phase are as small as about 0.3 and 2m, respectively. The _y, _f and _p are about 900 and 1650 MPa and 2.0% for the _L wires. The subsequent annealing causes an increase in _p as well as _y and _f and the attained values are about 1000 and 1700 MPa and 3.0% for Fe-10Ni-10Cr-6.5 Al-1.0C wire annealed at 773 K for 1 h owing to the precipitation strengthening of a very fine unidentified carbide and to a high density of dislocations and lath boundaries in the _L phase. Further annealing causes a significant decrease in _p through decomposition of _L to+M₇C₃+M₂₃C₆. Therefore, the high strength combined with relatively good ductility for the _L wires is interpreted as due to the suppression of the phase transformation of _L to a mixed structure of+M₇C₃+M₂₃C₆ by melt quenching.     

Group Actions on Binary Resilient Functions

Let G_n,t be the subgroup of GL(n,₂) that stabilizes {x₂ⁿ:|x|t}. We determine G_n,t explicitly: For 1tn–2, G_n,t=S_n when t is odd and G_n,t=S_n, when t is even, where S_n<GL(n,₂) is the symmetric group of degree n and GL(n,₂) is a particular involution. Let _n,t be the set of all binary t-resilient functions defined on ₂ⁿ. We show that the subgroup ₂ⁿ(G_n,tG_n,n–1–t)<AGL(n,₂) acts on _n,t/₂. We determine the representatives and sizes of the conjugacy classes of ₂ⁿS_n and ₂ⁿS_n,. These results allow us to compute the number of orbits of _n,t/₂ under the above group action for (n,t)=(5,1) and (6,2). Keywords:General linear group, Affine linear group, Resilient function.     

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.     

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.     

Correlation of burst pressure of GRP cylinders with the stress wave factor

Glass fibre-reinforced plastic (GRP) cylinders are increasingly used for highly stressed structural elements. The higher the demands on the materials, the higher are the fault detection requirements to be met by non-destructive materials testing methods. Acousto-ultrasonics is a valuable aid for the non-destructive evaluation of GRP composite materials, because it may be the answer to evaluating effects of subtle defects in composites. The aim of the research is to evaluate the burst pressure of GRP cylinders by acousto-ultrasonics techniques. The theoretical results have been found to be in good agreement with the experimental values. Hence the results strongly suggest that stress wave factor measurements can be exploited successfully to predict burst pressure of GRP cylinders.Nomenclature P Internal pressure, kgf cm^–2 - d Internal diameter, cm - t Thickness of cylinder, cm - (N ,N ,N ) Resultant forces, kgf - (M ,M ,M ) Moments, kg cm - [A] Extensional stiffness matrix - [B] Bending stretching coupling matrix - [D] Flexural stiffness matrix - ( ⁰ , ⁰ , ⁰ ) Midplane strains - (k ,k ,k ) Curvatures - n Number of laminae - Z Distance from midplane, cm - _u Ultimate tensile strength of GRP composite, kg cm^–2 - S _W Stress wave factor - m Material parameter - Filament winding angle     

Structure, Electronic Spectrum, and Chemical Bonding of Fullerene-like Nanoparticles Based on MB2(M = Mg, Al, Sc, Ti) Layered Diborides

The structure, electronic spectrum, and interatomic interaction parameters of _n B_2n (n = 10, 30, 90, 120, 160; M = Mg, Al, Sc, Ti) fullerene-like molecules based on MB₂ layered diborides are assessed using quantum-chemical modeling and are analyzed in relation to the atomic configuration, size, and chemical composition of _n B_2n . The electronic structure of concentric nanoparticles consisting of _n B_2n cage molecules having identical (₁₀B₂₀@₉₀B₁₈₀) or different (₁₀B₂₀@₉₀B₁₈₀, where M, M = Mg, Al) compositions is considered. The results are compared with the electronic properties of crystalline MB₂ phases.     

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.

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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.

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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     

Experimental evaluation of relative mode parameters in the irregular earth-to-ionosphere waveguide

Conclusions A model for representing the propagation of superlong waves was selected. Certain relative mode parameters ()₁, ()₂, ()₃, (V)₁, (V)₂, (V)₃, C₁, C₂, and C₃ can be used in order to account for the time-measurement error produced as a resuit of the double-mode signal propagation, to determine in a semiempirical manner the ionosphere's effective reflection height at night and in the daytime, to calculate and apply signal-propagation corrections which take into account phase velocity changes due to variations in the ionosphere height from day to day, and to calculate the fields of transition paths.Translated from Izmeritel'naya Tekhnika, No. 8, pp. 75–78, August, 1974.     

Transient thermal stress analysis of multilayered hollow cylinder

Summary This paper deals with the transient response of one-dimensional axisymmetric quasistatic coupled thermoelastic problems. Laplace transform and finite difference methods are used to analyze the problems. Using the Laplace transform with respect to time, the general solutions of the governing equations are obtained in the transform domain. The solution is obtained by using the matrix similarity transformation and inverse Laplace transform. We obtain solutions for the temperature and thermal stress distribution in a transient state. Moreover, the computational procedures established in this article can solve the generalized thermoelasticity problem for a multilayered hollow cylinder with orthotropic material properties.Nomenclature Lame's constant - density - C _v specific heat - k _r ,k radial and circumferential thermal conductivity - _r , linear radial and circumferential thermal expansion coefficient - E _r ,E radial and circumferential Young's modulus - v _r Poisson's ratio - ₀ reference temperature - ,T dimensional and nondimensional temperature - r ^*,r dimensional and nondimensional radial coordinate - ,t dimensional and nondimensional time - _r ^* , _r dimensional and nondimensional radial stress - ^* , dimensional and nondimensional circumferential stress - U, u dimensional and nondimensional radial component of displacement     

Dielectric properties of some hot-pressed nitrogen ceramics

The dielectric properties of some hot-pressed nitrogen ceramics have been measured at room temperature over the frequency range 200 Hz to 75 MHz and also at 9.3 GHz; low frequency measurements were also made at temperatures up to 500° C. The materials examined were Si₃N₄, 5.0 wt % MgO/Si₃N₄ and two sialons Si_(6–z)·Al _z ·O_z·N_(8–z) havingz = 4.0 and 3.2 respectively. At room temperature, the variation of the real part of the conductivity with frequency over the range 200 Hz to 9.3 GHz followed () ⁿ, withn = 0.9. The dielectric constant , and loss tan , both fell slightly over this frequency range, the average values at 10⁵ Hz being about 9.5 and 5.5 × 10^–3, respectively. The data fits well with the universal dielectric law, ^–1 (n < 1) and approximately fits the Kramers-Kronig relation ()/(() – = cot(n/2). This behaviour applies also at temperatures up to 500° C except that the value ofn decreases as the temperature increases. The effects may be caused by either dipolar or hopping charge phenomena.     

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.     

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.     

Effect of precipitate type and morphology on high-temperature creep and internal stress in Al-Li based alloys

The tensile creep of a series of aluminium-lithium-based alloys, two binary alloys containing precipitate, and the 2090 alloy containing and T₁ precipitate, has been studied over a range of stresses at 150°C. In some cases the internal stress developed during creep has been determined using the strain transient dip test. The results have been compared with similar data previously obtained for the 8090 alloy containing and S precipitates. The solid solution alloy and the binary alloy containing shearable particles exhibited normal Class II behaviour, with the development of sub-grains and a stress dependence of the creep rate given by a single stress exponent,n, between 4 and 5 at all applied stresses. The alloys containing particles not easily sheared by dislocations, coarse , S and T₁, exhibited similar stress dependencies of the creep rate at low stresses but exhibited large values ofn, between 18 and 35 at high stresses. The internal stress, _i, in these alloys was found to be approximately constant at high stresses possibly due to partial shearing of the coarse , T₁, and the S on sub-boundaries. The stress dependence of the minimum creep rate, , could be represented at all applied stresses, _a, by , where (_a–_i) is the effective stress driving dislocations during creep, andn is a single stress exponent of between 5 and 6 for all applied stresses. The internal stress, which increases with applied stress, at least at a low applied stress, arises from inhomogeneity of plastic deformation, due to hard sub-boundaries or hard particles which are Orowan looped. These two types of contribution to the internal stress are of similar magnitude in the alloys containing coarse and T₁ but the majority of the internal stress in the 8090 alloy may arise as a result of the hardening of sub-boundaries by the S precipitate.     

Stability of the nonequilibrium state of a superconductor irradiated by an electromagnetic field

Irradiation of a superconductor by an electromagnetic field with a frequency ₀ larger than twice the energy gap (order parameter) decreases the order parameter . We obtain the quasiparticle distribution function n and the dependence of the order parameter on the power of the electromagnetic field P by solving numerically the kinetic equations for n and in the steady state. We take ₀/₀ = 2.1, 8, and 20, where ₀ is the equilibrium value of the order parameter at T = 0 K. In the examples considered the dependence of on the pumping power P becomes double-valued above a critical power. We allow phonons also to be out of thermal equilibrium. To discuss the stability of the steady state thus obtained, we derive kinetic equations for small deviations of the quasiparticle distribution function and the order parameter from the steady state n and by means of the nonequilibrium Green's function theory. Assuming n, exp(i kr – t), (k) is computed using n _s/, where n _sis the steadystate quasiparticle distribution function for arbitrary . It is concluded in general that the steady state on the upper branch ( > _{c 2}) is stable with respect to both spatially homogeneous and inhomogeneous fluctuations, and the lower branch ( > _{c 2}) is unstable; _{c 2}is the value where the upper and lower branches of (P) coalesce.This work is partly supported by a Grant-in-Aid for Special Project Research from the Ministry of Education, Science and Culture of Japan.     

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.     

Biaxial dielectric properties of phenyl ester ferroelectric liquid crystal mixture

Dielectric and electro-optic properties of phenyl ester FLC mixture have been studied in detail. Dielectric relatation spectroscopy was used to study the molecular dynamics and dipolar ordering. In the SmA^* phase, this is accompanied by a sharp increase in the dielectric strength _s on approaching T _c. At such high frequency (2 MHz) is usually negative in the SmC^* and SmA^* phase. In the N^* phase, at lower frequencies, had a weakly positive value. In the SmC^* phase, is positive and its maximum value is less than 0.1. The dielectric biaxiality is discussed as an order parameter of the tilted smectic phase. It is verified that if the tilt angle increases according to (T _C – T), the biaxiality increases according to (T _C – T)². A critical exponent for and are 0.27 and 0.54, respectively. The rotational viscosity for soft mode is of 10 Nsec/m² in the SmA^* phase. The activation energy for the rotational dynamics of Goldstone mode is estimated to be 1.4 eV from an Arrhenius plot. Optical response time is of about 50 s at room temperature in SmC^* phase, and is on the order of 10 s in the N^* phase and almost independent of the applied field.     

Torsional boundary layer effects in shells of revolution undergoing large axisymmetric deformation

Numerical and asymptotic solutions are developed to the equations governing large torsional, axisymmetric deformation of rubberlike shells of revolution. The shell equations include large-strain geometric and material nonlinearities, transverse shear deformation, transverse normal stress and strain, and torsion. Both analyses allow ready incorporation of different strain-energy density functions. In the asymptotic analysis, the interior solution corresponds to that of nonlinear membrane theory and contains a primary boundary layer. The edge-zone solution gives a secondary boundary layer that, for large strain, divides into a bending-twisting moment component and a torsional-membrane component. The boundary layer behavior is illustrated for a clamped neo-Hookean cylinder subjected to internal pressure and axial torque.List of symbols Latin symbols a General dependent variable - a ^(mn) Terms of the asymptotic expansion of a(x) - b Characteristic length - c Scalar curvature components in the normal direction - c , c , , c Cosine of , respectively - C Material constant with units of a Young's modulus - e _i Deformed local orthonormal basis associated with (, s, n)(x ₁, x ₂, x ₃) coordinates - Undeformed cylindrical coordinate basis - Intermediate coordinate basis - g Shear correction factor - H Horizontal stress resultants - l ₁ Strain invariant - k Scalar curvature components - L Undeformed cylinder length - M Moment resultants - M _r, M , M _z Moment resultant components in the basis - N Membrane stress resultants - p Internal pressure - p _H, p _v Horizontal and vertical surface loads, respectively - p _i Thickness-averaged surface tractions - Q Transverse shear stress resultants - , r Radial coordinate prior to, after deformation - R Undeformed cylinder radius - , s Meridional coordinate prior to, after deformation - s , s _x, , s Sine of , respectively - , S Reference surface prior to, after deformation - S ₁, S ₂ Shear stress resultants parallel to the reference surface - S ₃ Average transverse normal stress resultant - t Undformed shell thickness - T Axial torque - V Vertical stress resultants - w Two-dimensional strain-energy density function - w _n Terms in expansion for w - W Three-dimensional strain-energy density function - x Undeformed axial coordinate in cylinder - , z Axial coordinate prior to, after deformation     

Thermal Conductivity of Sm3S4 System with Mixed Valence Sm Ions

The thermal conductivity () and electrical resistivity () of mixed-valence compound Sm₃S₄ have been measured in the temperature range 5 to 300 K. The present results and those presented previously [1] for the thermal conductivity between 80 to 850 K are interpreted in terms of the temperature-dependent fluctuating valence of Sm ions. Sm₃S₄ crystallizes in the cubic Th₃P₄ structure, and the cations with different valences occupy equivalent lattice sites. Divalent and trivalent Sm ions are randomly distributed in the ratio of 1:2 over all possible crystallographic cation positions (Sm²⁺ ₂Sm³⁺ ₂S^2– ₄). The behavior of the Sm₃S₄ lattice thermal conductivity _ph is extraordinary since valences of Sm ions are fluctuating (Sm³⁺Sm²⁺) with a temperature dependent frequency. In the interval 20 to 50 K (low hopping frequencies), _ph of Sm₃S₄ varies as _ph T ^–1 (it is similar to materials with static distribution of cations with different valences): at 95 to 300 K (average hopping frequencies 10⁷ to 10¹¹ Hz), _ph changes as _ph T ^–0.3 (it is similar to materials with defects). Defects in Sm₃S₄ appear because of local strains in the lattice by the electrons hopping from Sm²⁺ ions (with big ionic radii) to Sm³⁺ ions (with small ionic radii) and back (Sm²⁺Sm³⁺), at T>300 K (high hopping frequencies), _ph becomes similar to materials with homogenous mixed valence states [1].