Boundary Slab Research Articles

Influence of variable viscosity and gravity fluctuation on double diffusive convection in a fluid layer with boundary slab of finite conductivity

The linear stability analysis is carried out for the onset of double-diffusive convection in a fluid layer with a boundary slab along with temperature-dependent viscosity and gravity fluctuation. The authors proposed three types of gravity fluctuation. We considered three cases of gravity field fluctuation: (a) linear and (b)parabolic and (c) cubic. An analytical solution for the subsequent problem is acquired through the perturbation technique. The findings demonstrate that the viscosity variation parameter, the thermal conductivity ratio, the gravity parameter, the depth ratio, and the soret parameter accelerate the start of convection, while the increasing Lewis number slow down the convective motion. Additionally, the system was found to be more stable for the linear type of gravity field fluctuation and more unstable for the cubic type of gravity field fluctuation.

Inversion domain boundaries in Mn and Al dual‐doped ZnO: Atomic structure and electronic properties

AbstractThe atomic and electronic structures of inversion domain boundaries in Mn‐Al dual‐doped ZnO (Zn0.89Mn0.1Al0.01O) have been investigated. Using atomic‐resolution scanning transmission electron microscopy, a head‐to‐head c‐axis configuration and cation stacking sequence of αβαβ|γ|αβαβ along the c‐axis were observed at the basal‐plane inversion domain boundary. Energy‐dispersive X‐ray spectroscopy and electron energy‐loss spectroscopy revealed significant localization of Mn and minor localization of Al at the basal‐plane inversion domain boundary. Based on experimental findings, a Mn‐doped basal‐plane inversion domain boundary slab model was constructed and refined by first principles calculations. The model is in agreement with atomic‐resolution images. The local electronic density of states of the slab model basal‐plane inversion domain boundary shows a hybridization of the Mn d and O p states within the valence band and localized Mn d states in the conduction band. The thermoelectric properties of Zn0.99−xMnxAl0.01O ceramics have been reported in a previous work. In this work, the effects of inversion domain boundaries on the thermoelectric properties are discussed. In comparison to Zn0.99−xMnxAl0.01O ceramics with x≤0.05, inversion domain boundaries in Zn0.89Mn0.1Al0.01O caused thermal and electrical conductivity reduction due to interface scattering of phonons and electrons. The Seebeck coefficient increased, suggesting electron filtering at inversion domain boundaries.

The Harrison diffusion kinetics regimes in solute grain boundary diffusion

Knowledge of the limits of the principal Harrison kinetics regimes (Types A, B and C) for grain boundary diffusion is very important for the correct analysis of depth profiles in a tracer diffusion experiment. These regimes for self‐diffusion have been extensively studied in the past by making use of the phenomenological lattice Monte Carlo (LMC) method with the result that the limits are now well established. However, the relationship of these self‐diffusion limits to the corresponding ones for solute diffusion in the presence of solute segregation to the grain boundaries remains unclear. In the present study, the influence of solute segregation on the limits was investigated with the LMC method for the well‐known parallel grain boundary slab model by showing the equivalence of two diffusion models. It is shown which diffusion parameters are useful for identifying the limits of the Harrison kinetics regimes for solute grain boundary diffusion. It is also shown how the measured segregation factor from the diffusion experiment in the Harrison Type‐B kinetics regime may differ from the global segregation factor.

Investigation of Harrison Type-A, B and Intermediate AB Kinetics Regimes in Grain Boundary Diffusion

Recently, the transition point between the Harrison Type-A to Type-B kinetics regimes as well as the emerging intermediate AB transition regime have been analysed in detail by making use of Lattice Monte Carlo simulations of tracer depth concentration profiles as a function of diffusion time and distance between grain boundaries e.g. [7-9]. The principal model in this area has been the grain boundary slab model. However, depending on the diffusion time and grain size a given tracer atom can be expected to cross a number of grain boundaries in its diffusion time. This has recently been taken into account in square and cubic grain models for determining the limit of the Harrison Type-A regime [1]. In the present study, we determine the limits of the intermediate AB transition regime where we have used the Lattice Monte Carlo method to analyse the tails of tracer concentration depth profiles. The applicability of different solutions for the grain boundary diffusion analysis is numerically investigated for the 3D model. The solutions are those by Whipple-Le Claire [12,13] and Suzuoka [11], Bokstein, Magidson and Svetlov [15], Levine and MacCallum [14] for the type B kinetic regime and that by Divinski and Larikov [2] for the intermediate Type-AB regime. We also review the progress that has been made concerning the limits of the various Harrison regimes supplemented with the results of the present simulations. An empirical factor of 1.5 should be applied when Suzuoka or Whipple-Le Clair solutions are applied to the analysis of the tracer diffusion profile, tail section, in the polycrystalline material and an empirical factor of 2.0 should be applied when Bokshtein-Magidson-Svetlov solution is applied to the analysis of the tracer diffusion problem in the polycrystalline material.

Analysis of kinetics regimes in grain boundary self-diffusion†

The evolution of self-diffusion concentration depth profiles into a bulk polycrystalline material from a thin-film tracer source was studied using the lattice Monte Carlo method. The onset of the Type-B kinetics regime from the Type-A kinetics regime was investigated for a cubic grain model, which can be expected to capture the three-dimensional nature of the problem better than the usual grain boundary slab model. The solutions of Whipple–Le Claire (derived for the constant source condition), Suzuoka (derived for the instantaneous source condition), Bokstein and colleagues (derived for the constant source condition) and Levine and MacCallum (derived for the constant source condition) are tested. All these solutions describe the tail region of the profiles well for this model (provided that a simple empirical factor in the case of the first three solutions is introduced). The intermediate Type-AB kinetics regime proposed by Divinski and Larikov between the Type-A and Type-B kinetics regimes was also investigated but could not be located from analyses of best-fit exponents. Forcing the fitting nonetheless to the tail regions shows that their analysis needs some further refinement before application to this model. †This paper is dedicated to the memory of the late Alan Le Claire.

Exploration of the Transition from Harrison Type-A Kinetics to Type-B Kinetics Regimes in Grain Boundary Diffusion

We model the grain boundary tracer diffusion problem by constructing a 3D structure consisting of cubic grains each of equal volume. We build the structure in such a way that no four cubes have a common edge. It is shown that the transition point between Harrison Type-A and Type-B kinetics regimes occurs at a diffusant diffusion length roughly an order of magnitude smaller than for the extensively studied case of parallel grain boundary slabs. For two dimensional squares the transition point occurs at a diffusion length roughly a factor of five smaller than for parallel grain boundary slabs. Thus we can draw the conclusion that dimensionality and geometric shape are both important factors in the parametric analysis of the grain boundary diffusion problem.

Bridging Different Length and Time Scales in Diffusion Problems Using a Lattice Monte Carlo Method

In this paper, we show how lattice–based random walks of virtual particles directed by Monte Carlo methods (Lattice Monte Carlo) can be used to address a variety of complex phenomenologically mass diffusion problems. Emphasis is put on the practical details of doing the calculations. It is shown how concentration depth profiles can be determined: this is exemplified with diffusion in the presence of isolated dislocation pipes, grain boundary slabs, and oxygen segregation at interfaces in metal-ceramic oxide composites. It is also shown how effective diffusivities can be determined in materials. We also show how temperature profiles and the effective thermal conductivity can be determined for the thermal diffusion analogue of mass diffusion. A detailed comparison is made in one case with the results of the Finite Element method.

In-Situ Load Testing: A Theoretical Procedure to Design a Diagnostic Cyclic Load Test on a Reinforced Concrete Two-Way Slab Floor System

The objective of this paper is to showcase to an engineer who is considering performing a diagnostic cyclic load test a theoretical procedure for determining the patch load, which when applied to a two-way reinforced concrete (RC) slab floor system would generate internal forces at critical locations equal to those resulting from the uniformly distributed load. This procedure should also help the practitioner to define a representative model of the structure and to update the magnitude of the target load at the end of each loading and unloading cycle by means of a real-time evaluation of boundary conditions and slab stiffness. The routine to design a cyclic load test is described theoretically first and then validated with the results of a load test on a concrete two-way RC slab floor system. Introduction The current role of testing within structural engineering has gained increasing importance, as it can now be applied to every phase of the structure’s life because of innovative materials and new design approaches. By focusing on either the preliminary testing of a new structure or the necessary control checks prior to assessing the strength of an existing one, in-situ load testing can determine the real behavior of the structure under the existing loading conditions. Accordingly, researchers can have an overall, accurate understanding of the mechanical properties of the structural members. In the United States of America, the current American Concrete Institute (ACI) 318 Building Code [1] provides requirements for load testing of concrete structures. ACI Committee 437 [2] proposes a diagnostic cyclic load (DCL) testing procedure consisting of the application of patch loads in a quasi-static way to the structural member according to loading and unloading cycles. Patch load magnitude and distribution shall simulate the uniformly distributed load defined in the ACI 318 Building Code. The DCL protocol [3,4] defines three acceptance criteria that can be easily computed, in real time, for any structural member by simply checking its behavior under the test load (see Fig. 1 for necessary notation). Repeatability and Permanency represent the behavior of the structure during two identical load cycles; Deviation from linearity represents the measure of the nonlinear behavior of a member being tested. Repeatability = 100 95 B B max r A B max r % % Δ − Δ × ≥ Δ − Δ ; (1) Permanency = 100 10 B r B max % % Δ × ≤ Δ ; (2)

Forced convection in a bi-disperse porous medium channel: a conjugate problem

Forced convection in a plane channel filled with a saturated bi-disperse porous medium, coupled with conduction in plane slabs bounding the channel, is investigated analytically on the basis of a two-velocity, two-temperature model. It is found that the effect of the finite thermal resistance due to the slabs is to reduce both the heat transfer to the porous medium and the degree of local thermal non-equilibrium. An increase in value of the Péclet number leads to a decrease in the rate of exponential decay in the downstream direction but does not affect the value of a suitably defined Nusselt number. The dependence of Nusselt number on Biot number associated with the boundary slabs, the interphase heat exchange parameter, the interphase thermal conductivity ratio, the interphase effective permeability ratio, and the macroscopic void fraction, is investigated.

A calculation of diffusion parameters for Cu/Ta and Ta/Si interfaces in Cu/Ta/Si(1 1 1) structure

In this investigation, we have studied the elemental diffusion coefficients of the Cu/Ta and Ta/Si interfaces in the Cu/Ta/Si(1 1 1) structure. The diffusion parameters for Cu diffusion into the Ta barrier layer, Ta diffusion into the Si substrate and diffusion of Si atoms into the Ta layer have been calculated using conversion of RBS data to concentration-depth profile curves and the solution of Fick's equation based on a constant diffusing amount boundary conditions. Furthermore, by calculating grain boundary diffusion coefficients, we have estimated grain boundary slabs of the Ta layer at different temperatures. It was shown that, the width of grain boundary slabs in the Ta layer at 700°C allows a fast diffusion of Cu and Si atoms through the Ta barrier layer resulted in the copper silicide and TaSi 2 formation and consequently the barrier failure was observed at the temperature of 700°C in an N 2 environment for 30 min .

The transition from Harrison type-B to type-A kinetics in grain-boundary tracer diffusion

Abstract This paper is concerned with the lattice and grain boundary diffusivities that can be extracted from the tracer concentration depth profile resulting from diffusion of tracers from a thin film source in the presence of equally spaced parallel boundary slabs. We address this problem by mapping a grid over the phenomenologically conceived system and explore this grid with independent particles using Monte Carlo methods. It is shown that the transition from Harrison type-A kinetics (where the Hart equation provides the effective diffusivity) to Harrison type-B kinetics (where the lattice and grain boundary sections of the depth profile are delineated) occurs at a much smaller diffusion length than previously thought. In addition to the usual model where the mobility of tracers at the (surface) tracer source is matched to the immediate substrate, we also investigated a model which this mobility is made equal to the grain-boundary mobility. Similar behaviour was found.

The transition from Harrison type-B to type-A kinetics in grain-boundary tracer diffusion

Abstract This paper is concerned with the lattice and grain boundary diffusivities that can be extracted from the tracer concentration depth profile resulting from diffusion of tracers from a thin film source in the presence of equally spaced parallel boundary slabs. We address this problem by mapping a grid over the phenomenologically conceived system and explore this grid with independent particles using Monte Carlo methods. It is shown that the transition from Harrison type-A kinetics (where the Hart equation provides the effective diffusivity) to Harrison type-B kinetics (where the lattice and grain boundary sections of the depth profile are delineated) occurs at a much smaller diffusion length than previously thought. In addition to the usual model where the mobility of tracers at the (surface) tracer source is matched to the immediate substrate, we also investigated a model which this mobility is made equal to the grain-boundary mobility. Similar behaviour was found.

A Simulation Study of Tracer Diffusion Concentration Profiles Resulting from the Transition from Dislocation Pipes to a Grain Boundary Slab

ABSTRACTIn the present study we examine the well-known analysis in which the dislocation pipe diffusivity is determined by means of a grain boundary type analysis of the tail of a tracer concentration depth profile. We use a Monte Carlo grid method for testing the analysis. The results show that the analysis is really only satisfactory when the spacing between the dislocations is roughly twice the diffusion length (Dlt)½ where Dland t are the lattice diffusivity and time respectively.

Influence of viscosity variation on the stationary B�nard-Marangoni instability with a boundary slab of finite conductivity

The onset of stationary Benard-Marangoni instability in a variable-viscosity fluid layer with a boundary slab of finite conductivity is studied. The relations of the viscosity and surface tension of the fluid with the temperature are exponential and linear, respectively. The asymptotic solutions of the long wavelength, for small values of the conductivity and thickness of the solid, are achieved and are very well compared with the numerical results. As the viscosity ratio increases, the validity of the asymptotical solutions is extended for cases of larger values of the thermal conductivity and thickness ratios.

Twin boundary flux spinning in a high- Tc superconductor

The pinning potential due to a twin boundary in an anisotropic, continuous superconductor is calculated in a simple model. The model assumes the twin boundary to constitute a thin superconducting slab, different from and embedded in the host superconductor. Flux pinning is found to originate from two sources in several instances. One is an absolute minimum of the free energy. This type of pinning occurs when the twin boundary slab penetration length is larger than that of the host (weak link). The second pinning sources is a surface barrier (local minimum in the free energy) at the interface of two superconductors. This barrier depends, in certain limits, very strongly on the twin boundary thickness and the anisotropy of the host superconductor. The model yields an estimate for the critical current parallel to the twin boundary.

The analysis of dislocation pipe radius for diffusion.

Dislocation pipe radius for diffusion and the distribution are analyzed using combined an equivalent boundary slab model and a dislocation pipe model. Both models were applied to oxygen self-diffusion in MgO single crystal. The lattice diffusion coefficient Dl and the diffusion coefficient for oxygen diffusion along a dislocation, Dd, at 1350°C are obtained as Dl=1.17×10−20 and Dd=4.44×10−16 m2sec−1, respectively. Oxygen diffusion along the dislocation takes place within a pipe of radius 0.18 nm surrounding the dislocation. The theoretical results of dislocation structures, dislocation density d=3.2×1014 m−2 and subgrain size b=1.15 mum, are found to agree well with the electron-microscopic experiments by Moriyoshi and Ikegami (1985).

On rotating sphere-on-a-plate experiments and the question of whether high angle grain boundaries melt below bulk melting temperatures

The authors conclude that essentially all the boundaries in the rotating copper and silver sphere-on-a-plate experiments at 0.96 T/sub M/ and 0.99 T/sub M/ could not have been completely melted. Instead, it appears that they remained crystalline and that the rotations occurred because of the dependence of their energy on crystal misorientation. Possible situations include a variety of cases where the boundary is considerably disordered but where the atomic positions are still highly correlated with the atomic positions in the two grains adjoining the boundary slab. This conclusion is consistent with numerous previous interpretations of these experiments. The observation that all boundaries rotated into a relatively small number of discrete misorientations is also consistent with the conclusions that the boundary structures are related to the structures of the relatively low energy boundaries into which they rotated. Finally, the authors' conclusion is also consistent with the experimental results obtained by transmission electron microscopy where no evidence for boundary melting was found in different experiments with aluminum performed at 0.96 T/sub M/ and 0.999 T/sub M/.

Large-scale onset of Rayleigh-Bénard convection between well conducting slabs.

It is shown that neglecting the temperature dependence of thermal conductivities in the theory of Rayleigh-B\'enard instability is inconsistent. A model is presented which takes this dependence into account in the boundary slabs and also, to some extent, in the fluid. As a result, the horizontal scale at the onset of convection even between thick and well conducting slabs can be large as compared to the fluid thickness. A connection is suggested to chaotic behavior at the onset of convection.

Surface-Tension Driven Convection with Boundary Slab of Finite Conductivity

Surface-Tension Driven Convection with Boundary Slab of Finite Conductivity

The Rayleigh—Jeffreys problem with boundary slab of finite conductivity

Linear perturbation analysis is applied to the problem of the onset of convection in a horizontal layer of fluid heated uniformly from below, when the fluid is bounded below by a rigid plate of inlinite conductivity and above by a solid layer of finite conductivity and finite thickness. The critical Rayleigh number and wave-number are found for various thickness ratios and thermal conductivity ratios. Both numbers are reduced by the presence of a boundary of finite (rather than infinite) conductivity in qualitative agreement with the observation of Koschmieder (1966).