Simulation of interdiffusion processes in quasiternary systems of type MX/MY/MZ (β-class)

Diffusion processes in quasiternary systems are described by a diffusion matrix composed of a matrix covering the kinetic properties and a matrix describing thermodynamic influences by interaction parameters. The interdiffusion processes were simulated by a computer program and the calculated reaction paths were compared with earlier reported experimental data. It can be shown that thermodynamics governs the principal reaction paths, whereas the individual diffusion behavior is controlled by the kinetic matrix composed of tracer diffusion coefficients. Regions of uphill diffusion do occur not only in real, but even in ideal systems.     

The Kirkendall effect in single-phase multicomponent systems: dependence on drift and entropy distribution

This paper concerns interdiffusion in a diffusion couple and determination of the Kirkendall plane. The “entropy density” model is proposed in which the entropy is used to predict the position of the Kirkendall plane in a multicomponent system. It is shown that the marker position depends on the drift velocity and pressure field only. Application of the model is presented for ternary CoFeNi diffusion couples of three various initial compositions. The concentration profiles and entropy densities are calculated for each diffusion couple. The positions of the Kirkenadl planes are determined and compared with those obtained by velocity-curve and trajectory methods.     

On the accuracy of covariance matrix: Hessian versus Gauss-Newton methods in atmospheric remote sensing with infrared spectroscopy

Most retrieval schemes use a linear approximation of the radiative transfer function within each iteration as well as for error analysis. Like most standard methods, the improved Hessian method relies on a quadratic form of the cost function and linear approximation in the error analysis. Often, there is no robust criterion in determining step size that can be used to calculate covariance matrix by discrete perturbation of the cost function in the Hessian approach. The Hessian method improved recently, however, overcomes this problem by employing adaptive algorithm which uses small step sizes in steep directions and large step sizes in flat directions of the cost function. The results of retrievals of atmospheric trace gases from simulated limb emission spectra show that Gauss-Newton algorithm and the improved Hessian generally give nearly identical volume mixing ratios and error covariance matrices in the original state vector space. Due to interlevel correlations, however, the agreement in the uncertainities in the original state vector coordinate system is partly lost in a space in which the elements of state vector are independent after orthogonal coordinate transformation. The significant discrepancies between the estimated uncertainities by the two methods are found to be related with elements of state vector that are dominantly controlled by flattest eigenvector directions of the inverse covariance matrix. The improved Hessian method determines the uncertainities in those shallowest directions with better accuracy than Gauss-Newton approach. The performance of the Hessian method is also found to be better in resolving structures related to the shallowest eigenvector directions as revealed by better vertical resolutions in the retrieved profiles of the trace species.     

Surface exchange reactions and fast grain boundary diffusion in polycrystalline materials: Application of a spherical grain model

Laplace transforms of the solution functions to the diffusion equations for surface exchange reactions and fast grain boundary diffusion in polycrystalline materials of finite thickness have been derived by applying a spherical grain model. Diffusion profiles have been calculated for semi-infinite diffusion systems as well as thin films by application of numerical Laplace inversion. The surface exchange reaction at the surface of the sample (e.g. oxide ceramics) in contact with the constant diffusion source (e.g. gas phase) is assumed to be fairly slow such that the diffusion source is not in equilibrium with the surface during the diffusion anneal. Two limiting cases for the surface conditions are taken into account, viz. fast surface diffusion and a uniform ratio of the surface exchange coefficient/diffusion coefficient. The calculated profiles refer to Harrison's type-A diffusion kinetics. Apart from expressions for the effective diffusion coefficient, analogous relations for the effective surface exchange coefficient are proposed. Relaxation curves for the total amount of diffusant exchanged with the diffusion source are discussed in terms of the diameter of the spherical grains (average grain size), surface exchange coefficient, bulk and grain boundary diffusion coefficient, respectively.     

Diffusion paths in single-phase ternary metal systems

An analysis of diffusion paths in single-phase ternary metal systems Co–Fe–Ni and Cu–Fe–Ni on the basis of the phenomenological interdiffusion model using effective interdiffusion coefficients is presented. The peculiarities of practical application of effective interdiffusion coefficients of components for calculating diffusion paths in ternary systems are analysed. It is done on the basis of the relationship between effective interdiffusion coefficients and the diffusion paths. The results were found to be in good agreement with experimental data for the ternary systems Co–Ni–Fe and Cu–Ni–Fe. It is shown that deviation of the diffusion path from linearity in ternary single-phase diffusion couple in the system Cu–Ni–Fe mainly depends on the thermodynamic properties of the system.     

Theory of oxidation/reduction-induced valence transformations of metal ion dopants in oxide crystals mediated by oxide-vacancy diffusion: II. Kinetic analysis

We consider theoretically valence transformations of doping metal ions in oxide crystals induced by oxidation and reduction obtained by changes in the ambient oxygen partial pressure. Three types of oxygen vacancies are assumed to mediate transformations: neutral, singly ionized, and doubly ionized. In the companion part I paper we provide thermodynamic analyses yielding concentration relations among the oxygen vacancy, metal ions, holes and electrons, as functions of the ambient oxygen pressure. In the present companion part II paper we provide time dependent concentration profiles of the various species and reaction rate profiles. The diffusion exhibits a complex behavior; under some conditions, it may be described by a constant diffusivity, and is symmetric with respect to oxidation and reduction. However, under a wide range of conditions, the ionic state changes are highly asymmetric with respect to oxidation and reduction. For example, in the case of a neutral vacancy, a very narrow reaction front may establish during reduction. In the inverse (oxidation) process, however, the different species' profiles are quite smooth.     

A class of nonmixing dynamical systems with monotonic semigroup property

In order to illustrate the class of conservative dynamical systems for which a Boltzmann entropy can be obtained under finite coarse-graining [2], we consider dynamical systems defined by the shift transformation on K , where K is any finite set of integers. We give a class of non-Markovian invariant measures that verify the Chapman-Kolmogorov equation (equivalent to a Boltzmann entropy) for any positive stochastic matrix and that are ergodic but not weakly mixing.     

Entropy Generation during Head-On Interaction of Premixed Flames with Inert Walls within Turbulent Boundary Layers

The statistical behaviours of different entropy generation mechanisms in the head-on interaction of turbulent premixed flames with a chemically inert wall within turbulent boundary layers have been analysed using Direct Numerical Simulation data. The entropy generation characteristics in the case of head-on premixed flame interaction with an isothermal wall is compared to that for an adiabatic wall. It has been found that entropy generation due to chemical reaction, thermal diffusion and molecular mixing remain comparable when the flame is away from the wall for both wall boundary conditions. However, the wall boundary condition affects the entropy generation during flame-wall interaction. In the case of isothermal wall, the entropy generation due to chemical reaction vanishes because of flame quenching and the entropy generation due to thermal diffusion becomes the leading entropy generator at the wall. By contrast, the entropy generation due to thermal diffusion and molecular mixing decrease at the adiabatic wall because of the vanishing wall-normal components of the gradients of temperature and species mass/mole fractions. These differences have significant effects on the overall entropy generation rate during flame-wall interaction, which suggest that combustor wall cooling needs to be optimized from the point of view of structural integrity and thermodynamic irreversibility.     

Pseudo-binary and pseudo-ternary diffusion couple methods for estimation of the diffusion coefficients in multicomponent systems and high entropy alloys

The benefits of using the pseudo-binary and pseudo-ternary diffusion couple methods in multicomponent inhomogeneous systems are demonstrated by estimating different types of composition-dependent diffusion coefficients. These are important for understanding the basic atomic mechanism of diffusion and complex compositional evolutions. These were otherwise considered impossible during the last many decades. Without any options previously, sometimes the average values over a composition range of random choice were estimated, which are not the material constants but depend on the composition range and also the end member compositions. The steps and analyses for utilising the pseudo-binary and pseudo-ternary methods are first described in the Ni-Co-Fe-Mo system by producing the ideal diffusion profiles fulfilling the concepts behind these methods. Following, the discussion is extended to the systems related to medium (Ni-Co-Cr) and high (Ni-Co-Fe-Mn-Al) entropy alloys. In fact, this is the first report showing a correct experimental method that should be followed for the estimation of the interdiffusion and intrinsic diffusion coefficients in inhomogeneous high entropy alloys. In the end, the limitations of following these methods because of the generation of non-ideal diffusion profiles are discussed based on experimental results. The steps are also suggested to avoid such complications. These methods are easy to adopt for research engineers. Most importantly, these give an opportunity to validate the data estimated following newly proposed numerical methods by different groups with experimentally estimated diffusion coefficients, which were not possible earlier.     

Pattern of reaction diffusion fronts in laminar flows

Autocatalytic reaction between reacted and unreacted species may propagate as solitary waves, namely, at a constant front velocity and with a stationary concentration profile, resulting from a balance between molecular diffusion and chemical reaction. The effect of advective flow on the autocatalytic reaction between iodate and arsenous acid in cylindrical tubes and Hele-Shaw cells is analyzed experimentally and numerically using lattice Bhatnagar-Gross-Krook simulations. We do observe the existence of solitary waves with concentration profiles exhibiting a cusp and we delineate the eikonal and mixing regimes recently predicted.     

Pulse Evolution Characteristics in Self-Similar Mode-locked Fibre Laser

A self-similar mode locked fibre laser is studied based on a numerical model. By introducing a dimensionless factor k to characterize the pulse shape, the self-similar pulse evolution, formation and the temporal and spectral shape changes due to the elements in the cavity are investigated throughout the laser cavity. The results show that in the self-similar mode locked fibre laser, self-similar pulse is first formed in the single-mode fibre, which is then amplified in the gain fibre. Gain bandwidth has a small influence on pulse shape, so high energy self-similar pulse can be obtained after amplification. Because net cavity dispersion directly influences the pulse width as well as peak power after compression by a pair of gratings, which can determine the pulse self-similar evolution, it is very important to control the net cavity dispersion to a certain range to obtain self-similar pulses.     

Evolution of thermodynamic potentials in closed and open nanocrystalline systems: Ge-Si:Si(001) islands

An open (closed) system, in which matter is (not) exchanged through surface diffusion, was realized via growth kinetics. Epitaxially grown Si-Ge:Si (001) islands were annealed in different environments affecting the diffusivity of Si adatoms selectively. The evolution of the driving forces for intermixing while approaching the equilibrium was inferred from Synchrotron x-ray measurements of composition and strain. For the open system, intermixing due to the Si inflow from the wetting layer (reservoir) caused a decrease in the Ge content, leading to a lowering of the elastic energy and an increase in the mixing entropy. In contrast, for the closed system, while keeping the average Ge composition constant, atom rearrangement within the islands led to an increase in both elastic and entropic contributions. The Gibbs free energy decreased in both cases, despite the different evolution paths for the composition profiles.     

ps-LIF measurements of minor species concentration in a counterflow diffusion flame interacting with a vortex

Interactions of vortices and flame fronts may be considered as the basic structural elements of turbulent combustion. Additionally, they play an important role in flame instabilities as well as extinction and ignition processes. An ideal geometry to study these interactions is the counterflow diffusion burner with an additional actuator-driven nozzle for the generation of a vortex ring. This burner has already been well-characterized by other methods including CARS, LDA and PLIF. We present first quantitative measurements of minor species concentration in this flame using a short-pulse laser and time- and spatially resolved fluorescence detection with a streak camera. Quench-free OH concentrations are obtained by analysis of the time-resolved profiles. The high power density of the laser pulses allowed linewise detection of hydrogen using a three-photon excitation scheme. Simultaneously, shape and position of the vortex was monitored using two-dimensional detection of flame emissions. Spatially resolved concentration profiles of H and OH are presented for different interaction heights and times in the vortex. For steady flames, comparisons with model calculations are shown. Received: 19 July 2000 / Revised version: 13 December 2000 / Published online: 21 February 2001     

Kinetic Simulation of Nonequilibrium Kelvin-Helmholtz Instability

The recently developed discrete Boltzmann method(DBM), which is based on a set of uniform linear evolution equations and has high parallel efficiency, is employed to investigate the dynamic nonequilibrium process of Kelvin-Helmholtz instability(KHI). It is found that, the relaxation time always strengthens the global nonequilibrium(GNE), entropy of mixing, and free enthalpy of mixing. Specifically, as a combined effect of physical gradients and nonequilibrium area, the GNE intensity first increases but decreases during the whole life-cycle of KHI. The growth rate of entropy of mixing shows firstly reducing, then increasing, and finally decreasing trends during the KHI process. The trend of the free enthalpy of mixing is opposite to that of the entropy of mixing. Detailed explanations are:(i) Initially,binary diffusion smooths quickly the sharp gradient in the mole fraction, which results in a steeply decreasing mixing rate.(ii) Afterwards, the mixing process is significantly promoted by the increasing length of material interface in the evolution of the KHI.(iii) As physical gradients are smoothed due to the binary diffusion and dissipation, the mixing rate reduces and approaches zero in the final stage. Moreover, with the increasing Atwood number, the global strength of viscous stresses on the heavy(light) medium reduces(increases), because the heavy(light) medium has a relatively small(large) velocity change. Furthermore, for a smaller Atwood number, the peaks of nonequilibrium manifestations emerge earlier, the entropy of mixing and free enthalpy of mixing change faster, because the KHI initiates a higher growth rate.     

The effect of quaternary element on the thermodynamic parameters and structure of CuAlMn shape memory alloys

In this study, the Cu-based shape memory alloys were produced by arc melting. We have investigated the effects of the alloying elements on the characteristic transformation temperatures, enthalpy, entropy values, and the structure of Cu–Al–Mn ternary system. The evolution of the transformation temperatures was studied by the differential scanning calorimetry. The characteristic transformation temperatures can be controlled by the variations in the aluminum and manganese content. Additionally, the effect of magnesium and iron on the transformation temperatures and thermodynamic parameters was investigated in the Cu–Al–Mn ternary system. The addition of the magnesium decreases the characteristic transformation temperatures of the Cu–Al–Mn system, but that of the iron increases. The structural changes of the samples were studied by X-ray diffraction measurements and optical microscope observations. Due to the low solubility of the magnesium, the magnesium addition into the Cu–Al–Mn system forms precipitates in the matrix. It is evaluated that the transformation parameters of the CuAlMn shape memory alloys can be controlled by the change of the alloying elements and the weight percentages of alloying elements.     

Entropy production as a regularization factor in solving an inverse diffusion problem

Inverse diffusion problems allow the diffusion coefficients to be determined from experimental concentration profiles. Solutions of the inverse diffusion problem are unstable toward perturbations of the initial concentration profiles. By the example of inverse diffusion problem solution for a model binary system it is demonstrated that the use of the production entropy to minimize the discrepancy functional stabilizes the solution even for significant perturbations of the initial concentration profile. The choice of the entropy production for the smoothing component of the discrepancy functional is physically adequate to the formulated problem, and the entropy production can be used to solve inverse problems of heat and mass transfer. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 79–83, June, 2006.     

Rheology of interfacial protein-polysaccharide composites

The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their key part is a (dis)similarity matrix, according to which nodes are grouped. This study en- compasses the use of a stochastic matrix of a random walk, its mean first-passage time matrix, and a matrix of weighted paths count. We briefly indicate the connection between those quantities and propose substituting the maximal-entropy random walk for the previously chosen models. This unique random walk maximises the entropy of ensembles of paths of given length and endpoints, which results in equiprobability of those paths. We compare the performance of the selected algorithms on LFR benchmark graphs. The results show that the change in performance depends very strongly on the particular algorithm, and can lead to slight improvements as well as to significant deterioration.     

Binary and ternary metal carbides based upon Ti, Zr and Hf

Ab initio electronic structure calculations are employed to study the behavior of ternary alloy carbides based upon the metals Ti, Zr and Hf. Significant variations of the bulk modulus are found. The relative importance of each of the metals in influencing the cohesive properties of both binary and ternary metal carbides is discussed. A miscibility concept of ternary systems relative to the binary counterparts is considered at length and where it is argued that miscibility of the equilibrated or stable system is far different than for the metastable system as would be the case, for example, in a pressure synthesized alloy. From comparisons of two extremes of stable and metastable miscibility, speculation is made of extreme conditions as to how the ternary alloys can be achieved.