Non-stationary surface waves of “diverging circles” type on conic surfaces of hexagonal crystals

Summary Non-stationary surface waves of the diverging circles type propagating along a surface of a right circular cone from a hexagonal monocrystal are refered to as such, when a cone axis coincides with a crystal's axis of isotropy. It is shown that on a free surface of such a cone there are two types of waves: horizontally polarized surface waves (non-stationary waves of the whispering gallery type) and vertically polarized surface waves (non-stationary Rayleigh waves). Velocities of these waves are received and the attenuation of their intensities during propagation is investigated. As an example, we take a cone from a zinc oxide single crystal.     

The effect of substrate surface nature on texture formation in nickel oxide

X-ray diffraction was used to study the influence of surface finishing on polycrystalline nickel and its modification with ultra-fine dispersions of CeO2 on crystallographic texture development in NiO scales, grown at 1073 K in 760 torr oxygen for time periods up to75 h. Ni substrate characterized by 100 023 texture and surface with an atomic structure revealed by chemical polishing led to the formation of NiO with 100 013 texture, indicating an epitaxial growth.After applying CeO2 on the Ni surface prior to the oxidation, no essential changes in NiO texture were detected. When the Ni surface was deformed by mechanical polishing, NiO exhibited a fibre texture with a major component of 110 oriented along the growth direction. The presence of CeO2 on this substrate changed the dominant fibre axis to 100. The texture data are discussed in terms of the oxide microstructures and their growth kinetics. In particular, for CeO2-modified NiO scales with complex depth structure, the possible contribution of individual sublayers to the overall measured texture is estimated.     

Solution of Mixed Contact Problems in the Theory of Nonstationary Heat Conduction by the Method of Summation‐Integral Equations

The laws governing the development of spatial nonstationary temperature fields in a bounded cylinder and a halfspace where one of the end surfaces of the cylinder touches the surface of the halfspace in a circular region are determined. A solution of a mixed axisymmetric nonstationary problem of heat conduction is obtained in the region of Laplace transforms. In solution of this problem, there appear summationintegral equations with the parameter of the integral Laplace transform (Lparameter) and the parameter of the finite integral Hankel transform (Hparameter).     

Simultaneous measurement of surface tension and kinematic viscosity using thermal fluctuations

We have developed a surface laser-light scattering apparatus to measure simultaneously surface tension and kinematic viscosity. In this method, we can obtain the surface properties by the laser heterodyne detection of light scattered from thermally excited capillary waves (called ripplon), which are typically of low amplitude (1 nm) and a characteristic wavelength (100m). Two gratings (d=100 and 200m) were employed to select the wave number of the capillary waves and to produce a reference beam for heterodyne detection. It was found through an experimental study on water that this contact-free method has considerable potential for application to measurements under extreme conditions such as high temperatures and high pressures.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Duhamel integral and the operational-structural method of solution in nonstationary heat-conduction problems for regions of complicated shape

We propose an analytic method for solving nonstationary heat-conduction problems for regions of complicated shape with nonstationary boundary conditions and energy sources.Notation u temperature - density - thermal conductivity - c specific heat capacity - n number of coordinate functions - Fo=t(/cL) Fourier number - direction of the inner normal to the contour ₂ - L characteristic dimension of the plate - d thickness of the plate - sum of the total heat-transfer coefficients from the surface of the plate - Bi=L²/d=b² Biot number Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 40, No. 5, pp. 901–906, May, 1981.     

Kinetic theory of resistive states and electric oscillations in superconducting channels

The nature of resistive current states in a narrow superconducting channel at temperatures close to critical is discussed on the basis of the quantum kinetic theory for a generalized electron-hole density matrix. A new physical aspect of superconductivity is revealed: The superconductor displays peculiar properties in response to a nonequilibrium longitudinal electric field in the presence of a coherent source of electrons—a superconducting condensate. The microscopic structure of resistive states consists of a periodic alternation, along the uniform channel, of normal and superconducting regions described by singular solutions of the mean field equations. The singularities come from the discontinuity of the time derivative of the phase of the superconducting order parameter (phase slip) and provide voltage units through which the longitudinal electric field penetrates into the channel. In the paperI–V curves for resistive states are calculated and some nonstationary phenomena are pointed out.     

Theory of RF SQUIDs Operating in the Presence of Large Thermal Fluctuations

A comprehensive analytical theory is presented for non-hysteretic RF SQUIDs operating in the adiabatic mode in the presence of large thermal fluctuations. When 1 ( = 2LI_c/₀ is the hysteresis parameter, L is the SQUID inductance, I_c is the critical current of the Josephson junction, and ₀ is the flux quantum) the theory is applicable also for RF SQUIDs operating in the non-adiabatic mode. In contrast to previous theories in which the noise is treated perturbatively and which therefore are applicable only if the product 1 ( = 2k_BT/ ₀ I_c is the noise parameter, k_B is the Boltzmann constant, and T is the absolute temperature)—the case of small thermal fluctuations—the present theory is valid for around unity or higher. In the limit 0 the theory reproduces the results of small thermal fluctuations theories. It has been found that in the presence of large thermal fluctuations the screening current in the SQUID inductance is suppressed by a factor that increases with increasing . Taking into account this new basic fact, all SQUID characteristics (output signal, transfer function, noise spectral density and energy sensitivity) have been recalculated and a good agreement with experimental data has been obtained. It has been also found that RF SQUIDs can be operated with substantially higher values of the inductance and of the noise parameter than DC SQUIDs. These two aspects, which are of particular importance at liquid nitrogen temperature, make high T_c RF SQUIDs very attractive.     

Multi-length scale modeling of CVD of diamond Part II A combined atomic-scale/grain-scale analysis

Chemical vapor deposition of polycrystalline diamond films is studied by combining an atomic-scale kinetic Monte Carlo model with two one three-dimensional and one two-dimensional grain-scale models. The atomic-scale model is used to determine the growth rates of 111- and 100-oriented surface facets, the surface morphology of the facets and the extent of incorporation of the crystal defects. Using the atomic-scale modeling predicted growth rates for the 111- and 100-oriented facets, grain-scale modelling is carried out to determine the evolution of grain structure, surface morphology and crystallographic texture in the polycrystalline diamond films. It is found that depending on the relative growth rates of the 111- and 100-oriented facets, which can be controlled by selecting the CVD processing conditions, one can obtain either 110-textured films with a relatively smooth faceted surface or 100-textured films with a highly pronounced deep facets. In both cases, however, the film surface is composed entirely of the 111 facets. This findings are found to be fully consistent with the available experimental results.     

Analysis of Rheological Equations Involving More Than One Fractional Parameters by the Use of the Simplest Mechanical Systems Based on These Equations

The behaviour of rheological models containing more than onefractional derivative or fractional operator of fractional orders areinvestigated. All rheological models discussed can be separated intothree groups depending on magnitudes of the value_*/_* (where_* and _* are the orders ofsenior fractional derivatives of stress and strain, respectively): themodels are thermodynamically admissible only when_*/_* = 1 (the first group),thermodynamically compatible only for_*/_* 1 (the secondgroup) and, finally, thermodynamically well-conditioned both at_*/_* 1 and_*/_* > 1 (the third group).It is shown that, under nonstationary excitations, thebehaviour of the simplest mechanical systems (mechanical oscillators,finite and semi-infinite viscoelastic rods), based on the consideredrheological models, may be different (from the point of view ofthermodynamics) from that of the underlying rheological models. Thus,under impulse excitations, the mechanical models based on rheologicalmodels of the first and second groups become thermodynamicallyadmissible not only at_*/_* = 1 but alsowhen _*/_* < 1(mechanical models of group I), but mechanical models based onrheological models of the third group remain thermodynamicallywell-conditioned at the same magnitudes of rheological parameters as thecorresponding rheological models do (mechanical models of group II). Asthis takes place, group I mechanical models possess diffusion-wavefeatures, that is at_*/_*=1 the stress waves ina semi-infinite rod propagate at a finite speed, and the roots ofcharacteristic equations (for nonstationary vibrations of a mechanicaloscillator or a rod of finite length) as functions of the relaxation orretardation times, behave in a way similar to the characteristicequation roots of rheological models possessing instantaneous elasticity(models of the Maxwell type). When_*/_*<1, the stress wavesin a semi-infinite rod propagate instantaneously at infinitely largespeeds, and the roots of characteristic equations (under nonstationaryvibrations of a mechanical oscillator or a rod of finite length) asfunctions of relaxation times behave in a way similar to thecharacteristic equation roots of rheological models lackinginstantaneous elasticity (models of the Kelvin–Voigt type).Mechanical models from group II possess pure wave or pure diffusionfeatures at all magnitudes of_*/_*.     

Equation of state of3He near its liquid-vapor critical point

We report high-resolution measurements of the pressure coefficient (P/T) for³He in both the one-phase and two-phase regions close to the critical point. These include data on 40 isochores over the intervals–0.1t+0.1 and–0.2+0.2, wheret=(T–T _c )/T _c and =(– _c )/ _c . We have determined the discontinuity (P/T) of (P/T) between the one-phase and the two-phase regions along the coexistence curve as a function of . The asymptotic behavior of (1/) (P/T) versus near the critical point gives a power law with an exponent (+–1)^–1=1.39±0.02 for0.010.2 or–1×10 ^–2t–10 ^–6 , from which we deduce =1.14±0.01, using =0.361 determined from the shape of the coexistence curve. An analysis of the discontinuity (P/T) with a correction-to-scaling term gives =1.17±0.02. The quoted errors are fromstatistics alone. Furthermore, we combine our data with heat capacity results by Brown and Meyer to calculate (/T) _c as a function oft. In the two-phase region the slope (²/T ²)_c is different from that in the one-phase region. These findings are discussed in the light of the predictions from simple scaling and more refined theories and model calculations. For the isochores 0 we form a scaling plot to test whether the data follow simple scaling, which assumes antisymmetry of – ( _c ,t) as a function of on both sides of the critical isochore. We find that indeed this plot shows that the assumption of simple scaling holds reasonably well for our data over the ranget0.1. A fit of our data to the linear model approximation is obtained for0.10 andt0.02, giving a value of =1.16±0.02. Beyond this range, deviations between the fit and the data are greater than the experimental scatter. Finally we discuss the (P/T) data analysis for ⁴ He by Kierstead. A power law plot of (1/) P/T) versus belowT _c leads to =1.13±0.10. An analysis with a correction-to-scaling term gives =1.06±0.02. In contrast to ³ He, the slopes (²/T ²)_c above and belowT _c are only marginally different.Work supported by a grant from the National Science Foundation.     

Thermal shock resistance of miniaturized multilayer ceramic capacitors

The thermal shock resistance of miniaturized multilayer ceramic capacitors (MLCs), of sizes 0402, 0603, 0805 and 1206, was investigated by comparing the leakage currents before and after thermal shock. It was generally found that smaller capacitors have a higher thermal shock resistance than larger ones. The 0402 MLC possesses a thermal shock resistance in excess of 420 C. The linear interdependence of thermal shock resistance and reciprocal of half thickness, as predicted by conventional thermal shock analysis, was not observed. Instead, the thermal shock resistance of an MLC was found to be inversely proportional to the total area of its ceramic surface. This confirms that pre-existing flaws on the ceramic surface dominate the crack initiation process and are therefore primarily responsible for determining the thermal shock resistance of an MLC.     

Identification of Heat‐Exchange Processes in a Supersonic Spatial Flow Past Aircraft

Direct and inverse problems of heat exchange in a supersonic spatial flow past the front part of an aircraft in the form of a spherically blunted nose cone have been solved numerically. The prospects of using highheatconductivity materials and the blowing of the gascoolant for lowering the temperature on the surface of an aerodynamic body have been shown. A comparison of the solutions of the direct and inverse problems in one, two, and threedimensional formulations for various materials of the sheath has been made. The error in recovering the heat flow by the thinwalled method has been estimated.     

Some simple flows of a Johnson-Segalman fluid

Summary Unlike most other fluid models, the Johnson-Segalman fluid allows for a non-monotonic relationship between the shear stress and rate of shear in a simple shear flow for certain values of the material parameter. This has been used for explaining a phenomenon such as spurt. Here, we study three simple flows of a Johnson-Segalman fluid with a view towards understanding its response characteristics. We find that boundary conditions can have a very interesting effect on the regularity of the solution; changing them continuously leads to solutions that change their regularity. First, we consider the flow through a circular pipe and find solutions that have discontinuous velocity profiles which have been used to explain the phenomenon of spurt (cf. [10], [11]). Second, we consider the flow past an infinite porous plate and show that it will not admit solutions which have discontinuous velocity gradients, the solutions being necessarity smooth. Lastly, we study Poiseuille flow in a concentric annulus with porous boundaries. While spurt could be explained alternatively by allowing for stick-slip at the wall, the Johnson-Segalman model seems particularly suited in describing the appearance of shear-layers (cf. [13]).     

Geometric surface relief and the allotropic transformation in iron

Geometric surface relief effects have been observed in association with the allotropic transformation in iron. The selected-area electron channelling pattern technique has been used to establish that tent shaped geometric relief effects, common to single precipitate plates in Fe-C and Fe-C-X alloys, are also associated with similar single crystal morphologies in pure iron. These experimental observations extend to the allotropic transformation in iron the same rationale for the relationship of interfacial structure to surface relief effects that is known to apply in the instance of precipitation reactions. In addition it provides support for an earlier proposal that massive transformations can be subject to the same crystallographic constraints as precipitation processes.     

The effective surface energy of brittle materials

The effective surface energy of four brittle materials, alumina, poly(methylmethacrylate), glass, and graphite, is calculated from load/deflection curves of notched bars deformed in three-point bending. Two of the methods, which are commonly used in fracture mechanics studies,viz the modified Griffith treatment and the compliance analysis method, are concerned with the effective surface energy at the initiation of fracture, _I . The third method, the work of fracture test, is concerned with the mean effective surface energy over the whole fracture process, _F . The two estimates of _I give consistent values, and there is no systematic variation of _I with notch depth. Values of _F decrease with increasing notch depth as the fracture process becomes more controlled. For alumina _{I F} . For PMMA and glass _I > _F because of a multiplicity of crack sources during fracture initiation. For graphite _I < _F because of subsidiary cracking as fracture proceeds.     

Structure and Diamagnetic Properties of (Pb0.6SnyCu0.4 ? y)Sr2(Y1 ? xCax)Cu2Oz

The effect of Sn doping in (Pb_0.6Sn _y Cu_{0.4 – y} )Sr₂(Y_{1 – x} Ca _x )Cu₂O _z with 0 y 0.3 and 0 x 0.7 was investigated. It was established that a nearly pure 1212 phase can be obtained at 0 y 0.1 and 0 x 0.3. The obtained XRD patterns as well as the results of the EDX and ICP-AES analyses showed that Sn substitution is possible in the (Pb,Cu)-1212 phase. Superconductivity was observed at 0.4 x 0.7. The onset of the diamagnetic transitions varied from 10 to 30 K. The influence of the strong Pb deficiency on the superconducting properties of the samples was discussed.     

Zr surface diffusion in tetragonal yttria stabilized zirconia

The value for surface diffusivity of Zr tetragonal ZrO₂–3mol% Y₂O₃ has been calculated from measurements of surface area reduction and pore growth in powder compacts during sintering. The surface diffusivity thereby obtained can be described by D =5.52×10⁵ exp[–531(kJ mol^-1)/RT] m²/s, which is in reasonable agreement with values calculated by prior researchers from direct TEM observation of neck growth between touching particles.     

Calculation of the Nonstationary, Nonlinear Three‐Dimensional Problem of Heat Conduction by the Finite‐Element Method in Continuous Laser Heating

The process of nonstationary highintensity laser surface heating of a threedimensional body in the shape of a rectangular parallelepiped by a continuous laser with a normal distribution of the power density in the heating spot has been investigated numerically with the finiteelement method. Consideration has been given to the process of formation of the heataffected zone and its geometry. Thermal cycles of zonal points and their characteristics have been investigated.     

One‐Velocity Heterogeneous Flow Near a Cone

The selfsimilar flow of a onevelocity multicomponent mixture near a cone with an attached shock wave is studied within the framework of the generalizedequilibrium model of a heterogeneous medium. The flow generalizes the known Busemann solution for an ideal gas. Results of the numerical simulation of the problem of flow of a gas–liquid mixture past a cone are presented.     

R-curve behavior of layered silicon carbide ceramics with surface fine microstructure

By adjusting the : SiC phase ratios in the individual starting powders, a layered SiC consisting of surface and inner layers with distinctively different microstructures are produced by hot-pressing and subsequent annealing. The surface layer consisted of relatively fine, equiaxed -SiC grains, designed for high strength, while the inner layer consisted of elongated -SiC grains, designed for high toughness. By virtue of the common SiC phase and the same sintering aids (Al₂O₃-Y₂O₃), the interlayer interfaces are chemically compatible and strongly bonded. R-curve behavior of the layered SiC was measured and compared with the related monolithic materials. The layered SiC showed better damage tolerance than monolithic materials and stronger R-curve behavior than surface layer. This superior performance of layered SiC ceramics was attributed to the contribution of both high strength of the surface layer for small flaws and high toughness of the inner layer for larger flaws.