Bartek Wierzba

Entropy production during interdiffusion under internal stress

A theory of stress and elastic deformation during interdiffusion is presented. It is shown that it is consistent with the general Darken analysis and linear irreversible thermodynamics. Special consideration is given to local entropy production. An expression is derived for the rate of entropy production during interdiffusion and practical computations presented of the internal energy and entropy densities and the entropy production. It is shown that the entropy produced by the diffusion of mass is positive, , and it does not depend on the frame of reference. The results span the gap between the Darken method, linear irreversible thermodynamics and treatments by Larché, Cahn and Stephenson.

Chemical interdiffusion in binary systems; interface barriers and phase competition

The problem of simultaneous growth and competition of intermediate phases during reactive diffusion is formulated and solved. In this paper, we compare existing models of steady state reaction diffusion and introduce the new one basing on the bi-velocity method. We extend old problem and propose method based on material (lattice) fixed frame of reference. It allows computing the material velocity in the reacting system in which reactions at several moving interfaces occur. All reactions lead to the lattice shift due to the difference of intrinsic diffusivities and different molar volumes. The following peculiarities are taken into account: (1) the deviation from local equilibrium at all interfaces; (2) the mobilities of the components in the bulk and interphase zone; and (3) the molar volumes of the components. We show the kinetic of the reactions, the non parabolic regime, the multiphase scale growth and present the practical application of the method.

Diffusion, Drift and their interrelation through Volume Density

The evolution of the understanding of the mass transport phenomena in solids and liquids allows for the unification of phenomenological models. The central Darken problem is considered from the choice of the coordinate axes for diffusion, i.e. the definition of this mode of motion and the method of diffusion displacement is defined and measured. Eulers and Liouville theorems are used extensively in the analysis. The formula is derived for volume density conservation, i.e. the volume continuity equation. This fundamental formula defines the volume-fixed frame of reference in the multicomponent solid, gas and liquid solutions. The volume-fixed frame of reference is self-consistent with the foundations of linear irreversible thermodynamics, except that is recognises the need to add volume density to the usual list of extensive physical properties undergoing transport in every continuum. Proposed modifications are self-consistent with the literature dating back to Onsager, the experiments of Kirkendall, their interpretation by Darken and recent generalized formulations. It will be shown that the method can be used in mechano-chemistry and electro-mechano-chemistry.

A Morphology of Diffusion Zone from Entropy Production Calculations

Interdiffusion plays a significant role in the formation and stability of metallic joints and coatings. It is also of critical importance in designing advanced materials. Because commercial alloys are usually multicomponent, the key target is prediction of a complex morphology of the diffusion zone which grows between the alloys, alloy-coating, etc. In a two-component system, the diffusion zone can be composed of single-phase layers of the intermetallic compounds and solid solutions. The evolution of the composition and thicknesses of such layers are fairly well understood and consistent with the phase diagrams. The situation is qualitatively different in multicomponent systems. For example, the diffusion zone in a ternary system can be composed of single-and two-phase sublayers. Their number and thicknesses depend on the initial conditions, i.e. composition, component diffusivities and geometry of the system. The usual way of presenting the sequence of the layers and their compositions is by drawing adiffusion path which is, by definition, a mapping of the stationary concentrations onto the isothermal section of the equilibrium phase diagram. The diffusion path connects initial compositions of the diffusion couple and can go across the single-, two-and three-phase fields. It starts at the composition of one alloy and ends at the other. The possibility of mapping the concentration profiles onto the ternary isotherm has been postulated in one from the seventeen theorems by Kirkaldy and Brown [] for the diffusion path. The detailed presentation of all theorems was recently done by Morral []. Here we remind the reader only of the chosen ones (shown in italics).

Bi-velocity model of mass transport in two-phase zone of ternary system

Bi-velocity (Darken) method, which includes material drift and diffusion fluxes, is for the first time applied to describe mass transport in multiphase materials. The respective model is formulated in details and then applied for a ternary diffusion couple in which a two-phase zone can grow during isothermal diffusion. Thanks to the use of a phase-field order parameter, identified here with volume fraction of a chosen phase, the mass transport throughout both phases within a two-phase zone can be considered. The model allows smooth crossing of the type 1 boundary, which makes the mass transport equations valid in both single- and two-phase regions. The solution obtained for 1D geometry provides: (1) a diffusion path in the concentration triangle, (2) element-concentration profiles, (3) volume fractions of the phases in the two-phase zone and (4) drift-velocity distribution along x axis parallel to the mass transport. As an example, the interdiffusion in the diffusion couple of Type 0 boundary is modelled. The zigzag diffusion path is predicted and the profiles of the element concentrations are simulated. For the first time, the drift velocity for the diffusion in two-phase system is determined and correlated with the changes in volume fractions of the phases.

The Ni-Al-Zr Multiphase Diffusion Simulations

Abstract The generalized Darken method allows a quantitative description of diffusion mass transport in multi-phase materials. The method characterizes the diffusion zone by phase volume fractions. The results of the calculations are compared with experimental concentration’s profiles of nickel, zirconium and aluminum in zirconium doped aluminide coatings deposited on pure nickel by the PVD and CVD methods.

Effect of Ti and Ta on Oxidation Kinetic of Chromia Forming Ni-Base Superalloys in Ar-O2-Based Atmosphere

Abstract In the present study, two commercially available Ni-base superalloys, namely Rene 80 which contains Ti and IN 792 containing Ti and Ta, were investigated during isothermal oxidation at 1,050°C in Ar–20% O2 gas up to 50 h. It was found that IN 792 showed a slightly lower oxidation rate as compared to Rene 80. Also differences in oxide scale microstructures and thicknesses were found. Both alloys formed qualitatively similar oxide scales consisting of outer TiO2 on top of a Cr2O3 scale and internally oxidized Al2O3. The IN 792 formed a thinner oxide scale in general as well as a thinner outer TiO2 scale. Also the depth of the internally oxidized Al2O3 precipitates is smaller in case of IN 792. These findings were correlated with the formation of TiTaO4, which in turn hampered outer Ti and inward oxygen flux.

Surface preparation effect on oxidation kinetics of Ni-base superalloy

In the present study an oxidation behavior of commercially available Ni-base superalloy IN 713C with different surface finishing, namely polished up to 1 μm diamond paste (resulting in Ra = 0.023) and ground by SiC paper with 80 grit (Ra = 1.23), were investigated at 950°C in air. It was found that ground sample developed very thin, protective α-Al2O3 scale. Moreover, locally formation of θ-Al2O3 in the forms of spikes was observed. For the sample with polished surface formation of outer chromia scale accompanied with internal oxidation of aluminum was observed. Moreover, for specimen which does not form continuous alumina scale or sub-scale, the GD-OES depth profiles showed an enrichment of boron at the oxide scale/alloy interface. It was proposed that the formation of protective alumina scale on ground samples is caused by introducing the defects into the near-surface region of the material, which are an easy diffusion paths for the elements forming a protective oxide scales.

Void Formation during Diffusion – Two-Dimensional Approach

Abstract The final set of equations defining the interdiffusion process in solid state is presented. The model is supplemented by vacancy evolution equation. The competition between the Kirkendall shift, backstress effect and vacancy migration is considered. The proper diffusion flux based on the Nernst–Planck formula is proposed. As a result, the comparison of the experimental and calculated evolution of the void formation in the Fe-Pd diffusion couple is shown.

Bi-velocity Phase Field Method

In this paper we couple the bi-velocity with the phase field method. It deals with: (1) the different mobility of the components in the two-phase zone; (2) nonzero steps of molar volumes for each component from phase to phase and (3) the composition dependent interdiffusion coefficients. The method allows to determine the average stress field during the diffusion process, the kinetics of the reactions and estimate the entropy production. The paper presents the numerical computations of diffusion in th eNiAlCr system. The results can serve as a basis in designing gradient coatings of extended life time.