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1

A Diffusion Model of Binary Systems Controlled by Chemical Potential Gradient

Wróbel Marek, Burbelko Andriy

Journal of Casting & Materials Engineering

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2022

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Vol. 6, no. 2

39--44

EN

The paper presents a model of diffusion in a single phase with chemical potential gradient as the driving force of the process. Fick’s laws are strictly empirical and the assumption that the concentration gradients are the driving forces of diffusion is far from precise. Instead, the gradient of chemical potential μi of component i is the real driving force. The matter of governing equations of models that incorporate this approach will be raised and discussed in this article. One of more important features is the ability to acquire results where diffusion against the concentration gradient may occur. The presented model uses the Finite Difference Method (FDM) and employs the CALPHAD method to obtain chemical potentials. The calculations of chemical potential are carried out for instant conditions – temperature and composition – in the entire task domain by Thermo-Calc via a TQ-Interface. Then the heterogeneity of chemical potentials is translated into mass transfer for each individual element. Calculations of two modelling tasks for one-dimension diffusion field were carried out. First: isothermal conditions with linear initial composition distribution and second: constant temperature gradient with uniform chemical composition in the specimen. Results for two binary solid solutions: Fe-C and Fe-Si, in the FCC phase for the given tasks will be presented. Modelling allows us to estimate the time needed to reach a desired state in a particular equilibrium or quasi-equilibrium state. It also shows the path of the composition change during the process. This can be used to determine whether the system at some point is getting close to the formation of another phase due to significant deviation from its initial conditions.

2

Impact of Values of Diffusion Coefficient on Results of Diffusion Modelling Driven by Chemical Potential Gradien

Wróbel Marek, Burbelko Andriy

Archives of Foundry Engineering

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2022

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Vol. 22, iss. 3

81--90

EN

In the paper critical role of including the right material parameters, as input values for computer modelling, is stressed. The presented model of diffusion, based on chemical potential gradient, in order to perform calculations, requires a parameter called mobility, which can be calculated using the diffusion coefficient. When analysing the diffusion problem, it is a common practice to assume the diffusion coefficient to be a constant within the range of temperature and chemical composition considered. By doing so the calculations are considerably simplified at the cost of the accuracy of the results. In order to make a reasoned decision, whether this simplification is desirable for particular systems and conditions, its impact on the accuracy of calculations needs to be assessed. The paper presents such evaluation by comparing results of modelling with a constant value of diffusion coefficient to results where the dependency of Di on temperature, chemical composition or both are added. The results show how a given deviation of diffusivity is correlated with the change in the final results. Simulations were performed in a single dimension for the FCC phase in Fe-C, Fe-Si and Fe-Mn systems. Different initial compositions and temperature profiles were used.

3

Thermo-diffusion of a thick circular plate via modified Green–Naghdi models

Zenkour A. M.

Archives of Mechanics

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2020

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Vol. 72, nr 3

235--256

EN

This article presents the thermo-diffusion of an isotropic thick circular plate. The Green and Naghdi’s models including the energy dissipation are anticipated in their simple forms. Novel multi single/dual-phase-lag models with higher-order timederivatives are also provided to examine the thermo-diffusion response of the circular plate. The simple and refined forms of Green and Naghdi’s types II and III are investigated in this work. The closed-form solution of thermal diffusion governing equations is attained by taking into account the boundary conditions. A validation examples of outcomes are acceptable by comparing all quantities according to the discussing of all thermoelastic models. The refined forms of Green and Naghdi’s types II and III should be applied to get accurate outcomes.

4

Interaction due to thermodiffusive and mechanical sources in micropolar elastic medium

Kumar R., Kaushal S., Miglani A.

Journal of Technical Physics

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2009

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Vol. 50, no 4

317-342

EN

In this present paper, first the equations of generalized micropolar thermodiffusive medium, based on the theory of Lord and Shulman with one relaxation time are derived and then, deformation in a micropolar thermoelastic diffusive medium has been studied due to various sources. Laplace and Fourier transforms are used to solve the problem. The application of concentrated normal force, thermal point source and chemical potential point source has been considered to show the utility of the solution obtained. The transformed components of stress, temperature distribution and chemical potential are inverted numerically using a numerical inversion technique. The effect of micropolarity and diffusion on these quantities are presented graphically in order to illustrate and compare the analytical results. Some special cases of micropolarity and diffusion are also deduced.

5

Rola termodynamiki w inżynierii materiałowej

Kędzierski Z.

Hutnik, Wiadomości Hutnicze

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2004

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Vol. 71, nr 7-8

292-297

PL

Celem publikacji jest prezentacja potencjalnych mozliwości wykorzystania termodynamiki w inżynierii materiałowej. Na przykładzie dyfuzji wstępującej omówiono rolę potencjału chemicznego jako ogólnej siły pędnej dyfuzji. Zaprezentowae zostały podstawy teorii fluktuacji i niestabilności roztworów stałych. W części końcowej opisano problemy zwiazane z energia swobodną powierzchniową i termodynamiką powierzchni międzyfazowych.

EN

The aim of the paper is outline generally usefulness of application basic thermodynamic concepts to materials science and engineering. The importance of chemical potential as general driving forceof diffusion is shortly discussed and examples of uphill diffusion are presented and explained. The role of composition flucuation in phase transformation and spinodal decomposition is also discussed. Finally fundamental problems of interface thermodynamics and effects of interface energy on phase diagram are presented.