Study on the Growth of Nb3Sn Superconductor in Cu(Sn)/Nb Diffusion Couple

Nb3Sn growth following the bronze technique, (i.e. by interdiffusion between Cu(Sn) alloy (bronze) and Nb) is one of the important methodologies to produce this superconductor. In this study, we have addressed the confusion over the growth rate of the Nb3Sn phase. Furthermore, a possible explanation for the corrugated layer in the multifilamentary structure is discussed. Kirkendall marker experiments were conducted to study the relative mobilities of the species, which also explained the reason for finding pores in the product phase layer. Based on the parabolic growth constant at different temperatures, the activation energy for the growth is determined. We have further explained the dramatic increase in the growth rate of the prod

Dynamics of polar solvation: Route to single exponential relaxation via translational diffusion

A microscopic theoretical calculation of time-dependent solvation energy shows that the solvation of an ion or a dipole is dominated by a single relaxation time if the translational contribution to relaxation is significant.

Generalized Equation for Compression Ratio

For highly compressible normally consolidated saturated soil the compression index, Cc, is not constant over the entire pressure range. However, the ratio of the compression index and the initial specific volume, generally known as the compression ratio, appears to be constant. Thus settlement seems to depend on Cc/(1 + e) rather than Cc alone. Using the theoretical zero air voids line and the generalized compressibility equation for normally consolidated saturated soils, a generalized and simple equation for compression has been derived in the form: C'c = 0.003wL.

The Alfvén Wave Equation for Magnetospheric Plasmas

It is shown that besides the continuous spectrum which damps away as inverse power of time, the coupled Alfvén wave equation, which gives coupling between a shear Alfvén wave and a surface wave, can also admit a well behaved harmonic solution in the closed form for a set of initial conditions. This solution, though valid for finite time intervals, points out that the Alfvén surface waves can have a band of frequency (instead of a monochromatic frequency for a nonsheared magnetic field) within which the local field line resonance frequency can lie, and thus can excite magnetic pulsations with latitude-dependent frequency. By considering magnetic fields not only varying in magnitude but also in direction, it is shown that the time interval for the validity of the harmonic solution depend upon the angle between the magnetic field directions on either side of the magnetopause. For small values of the angle the time interval can become appreciably large.

Polarization Caging in Diffusion-Controlled Electron Transfer Reactions in Solution

In some bimolecular diffusion-controlled electron transfer (ET) reactions such as ion recombination (IR), both solvent polarization relaxation and the mutual diffusion of the reacting ion pair may determine the rate and even the yield of the reaction. However, a full treatment with these two reaction coordinates is a challenging task and has been left mostly unsolved. In this work, we address this problem by developing a dynamic theory by combining the ideas from ET reaction literature and barrierless chemical reactions. Two-dimensional coupled Smoluchowski equations are employed to compute the time evolution of joint probability distribution for the reactant (P-(1)(X,R,t)) and the product (p((2))(X,R,t)), where X, as is usual in ET reactions, describes the solvent polarization coordinate and R is the distance between the reacting ion pair. The reaction is described by a reaction line (sink) which is a function of X and R obtained by imposing a condition of equal energy on the initial and final states of a reacting ion pair. The resulting two-dimensional coupled equations of motion have been solved numerically using an alternate direction implicit (ADI) scheme (Peaceman and Rachford, J. Soc. Ind. Appl. Math. 1955, 3, 28). The results reveal interesting interplay between polarization relaxation and translational dynamics. The following new results have been obtained. (i) For solvents with slow longitudinal polarization relaxation, the escape probability decreases drastically as the polarization relaxation time increases. We attribute this to caging by polarization of the surrounding solvent, As expected, for the solvents having fast polarization relaxation, the escape probability is independent of the polarization relaxation time. (ii) In the slow relaxation limit, there is a significant dependence of escape probability and average rate on the initial solvent polarization, again displaying the effects of polarization caging. Escape probability increases, and the average rate decreases on increasing the initial polarization. Again, in the fast polarization relaxation limit, there is no effect of initial polarization on the escape probability and the average rate of IR. (iii) For normal and barrierless regions the dependence of escape probability and the rate of IR on initial polarization is stronger than in the inverted region. (iv) Because of the involvement of dynamics along R coordinate, the asymmetrical parabolic (that is, non-Marcus) energy gap dependence of the rate is observed.

Flow structure and heat transfer characteristics behind a diaphragm in the presence of a diffusion flame

The characteristics of the separated flow behind a diaphragm over a burning surface are investigated experimentally. This complex problem of practical significance involving recirculation, blowing and combustion reactions is studied in a two-dimensional combustion tunnel. The flame structure, recirculation patterns and heat transfer to the surface are presented for a range of values of free stream and fuel injection velocities as well as for different heights of the diaphragm. The trends of heat transfer vs axial distance are shown to be similar to those resulting from a non-reactive heated stream with a diaphragm. Treating the case of a boundary layer diffusion flame as that corresponding to the zero height of the diaphragm, the heat transfer augmentation due to recirculation is estimated. It is found that at considerable downstream distances (xfh > 3), the heat transfer rates with diaphragm overtake the rates from a developing boundary layer case. Flow visualization studies with particle track photography show that there are many similarities between the reactive and the non-reactive cases.

Probability Distribution of the Eigenvalues of the Random String Equation

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

A molecular dynamics study of cage-to-cage migration in sodium Y zeolite: role of surface-mediated diffusion

The details of cage-to-cage migration have been obtained from an analysis of the molecular dynamics trajectory of a probe adsorbate. It is observed that particles utilize the region within a radius of 2 angstrom from the window center but with diffusion taking place predominantly at 1.6 angstrom from the window center and a potential energy of nearly -12 kJ/mol. A barrier of about 0.5 kJ/mol is observed for surface-mediated diffusion. Surprisingly, for diffusion without surface mediation for a particle going from one cage center to another, there is an attractive well near the window instead of a barrier. At low adsorbate concentrations and room temperature, the predominant mode for cage-to-cage migration is surface-mediated diffusion. The analysis suggests that particles slide along the surface of the inner walls of the alpha-cages during migration from one cage to another.

Brownian motion of spins; generalized spin Langevin equation

We derive the Langevin equations for a spin interacting with a heat bath, starting from a fully dynamical treatment. The obtained equations are non-Markovian with multiplicative fluctuations and concommitant dissipative terms obeying the fluctuation-dissipation theorem. In the Markovian limit our equations reduce to the phenomenological equations proposed by Kubo and Hashitsume. The perturbative treatment on our equations lead to Landau-Lifshitz equations and to other known results in the literature.

Diffusion coefficients for selected binary liquid systems: cyclohexanes and n-alkyl alcohols

In the present work the integral diffusion coefficients are estimated by using the diaphragm cell technique. The diffusion coefficients are measured at various compositions for two sets binary systems: one of cyclohexane and n-paraffinic alcohols and the other of methylcyclohexane and n-paraffinic alcohols. The alcohols used are seven members of homologous series of n-paraffinic alcohols from ethanol to octanol. The maximum possible error in the experimental diffusion coefficient could be 8% for both the cyclohexane-n-alkyl alcohol system and methylcyclohexane-n-alkyl alcohol system. A correlation for each of the two sets of binary systems is given. The maximum deviation in the correlations was less than 6.5 and 3.5% for cyclohexane-n-alkyl alcohols and methylcyclohexane-n-alkyl alcohols, respectively.

Mutual diffusion coefficients of some binary liquid systems: benzene-n-alkyl alcohol

The mutual diffusion coefficients for binary liquid systems of benzene-n-alkyl alcohol at various compositions have been determined by the diaphragm cell method at 28-degrees-C. The alcohols used were the members of n-paraffinic alcohols ranging from C1 to C8. The maximum possible experimental error is 14%. The data were fitted with a generalized correlation, giving the deviation from the experimental data to within 2.75%, on average.

Rocking response of rectangular rigid blocks under random noise base excitations

The response of a rigid rectangular block resting on a rigid foundation and acted upon simultaneously by a horizontal and a vertical random white-noise excitation is considered. In the equation of motion, the energy dissipation is modeled through a viscous damping term. Under the assumption that the body does not topple, the steady-state joint probability density function of the rotation and the rotational velocity is obtained using the Fokker-Planck equation approach. Closed form solution is obtained for a specific combination of system parameters. A more general but approximate solution to the joint probability density function based on the method of equivalent non-linearization is also presented. Further, the problem of overturning of the block is approached in the framework of the diffusion methods for first passage failure studies. The overturning of the block is deemed incipient when the response trajectories in the phase plane cross the separatrix of the conservative unforced system. Expressions for the moments of first passage time are obtained via a series solution to the governing generalized Pontriagin-Vitt equations. Numerical results illustra- tive of the theoretical solutions are presented and their validity is examined through limited amount of digital simulations.

Large-amplitude chirped coherent phonons in tellurium mediated by ultrafast photoexcited carrier diffusion

We report femtosecond time-resolved reflectivity measurements of coherent phonons in tellurium performed over a wide range of temperatures (3-296 K) and pump-laser intensities. A totally symmetric A(1) coherent phonon at 3.6 THz responsible for the oscillations in the reflectivity data is observed to be strongly positively chirped (i.e., phonon time period decreases at longer pump-probe delay times) with increasing photoexcited carrier density, more so at lower temperatures. We show that the temperature dependence of the coherent phonon frequency is anomalous (i.e, increasing with increasing temperature) at high photoexcited carrier density due to electron-phonon interaction. At the highest photoexcited carrier density of (1.4 x 10(21) cm(-3) and the sample temperature of 3 K, the lattice displacement of the coherent phonon mode is estimated to be as high as similar to 0.24 angstrom. Numerical simulations based on coupled effects of optical absorption and carrier diffusion reveal that the diffusion of carriers dominates the nonoscillatory electronic part of the time-resolved reflectivity. Finally, using the pump-probe experiments at low carrier density of 6 x 10(18) cm(-3), we separate the phonon anharmonicity to obtain the electron-phonon coupling contribution to the phonon frequency and linewidth.

Impurity diffusion in bismuth single-crystals

Measurements of impurity diffusion of 86Rb, 90Sr, 133Ba, and 137Cs in single crystal Bi were carried out. Diffusion samples were prepared from single crystal Bi by ion implantation. About 1012-1013 ions were implanted, resulting in surface activities approx =104 cpm. After implantation, specimens were annealed for specified times at 220-265 deg C, and tracer penetration profiles were determined by an electrolytic method. A typical penetration profile for 137Cs in Bi showed a linear relationship for log C vs x in with Fick's law for volume diffusion. Laws of grain boundary diffusion were not obeyed and the order of magnitude of the penetration distances was much less than on a grain boundary mechanism. Results were interpreted in terms of a modified Fischer analysis using a kinetic trapping term. Effective half lengths for trapping at a twin boundary were determined for each impurity.