Papers by Keyword: Fick's Law

Abstract: Multicomponent diffusion in metallic melts is a very important phenomenon during the solidification/casting process of the metallic alloys. However, there exist extremely limited reports on the diffusivity information in multicomponent metallic liquids. In this chapter, a universal and effective phenomenological approach to predict the composition– and temperature–dependent diffusivities in liquid multicomponent systems is systematically proposed. The presently proposed phenomenological method is then adopted to construct the diffusivity/mobility databases of liquid solders, cemented carbides, Co–Cr–Fe–Mn–Ni high entropy alloys and Al–Ce–Ni alloys. Then, the accurate diffusivity/mobility data are further utilized to perform the simulations of the dissolutions of the substrate into the solders, the gradient layer formation of the cemented carbides, the diffusion behavior of liquid Co–Cr–Fe–Mn–Ni high entropy alloys and the rapid solidification of Al–Ce–Ni system. The simulated results indicate that the presently proposed phenomenological method is applicable to investigate the diffusion kinetics in multicomponent metallic melts.

Abstract: In order to estimate the impact of the degree of water saturation of concrete to chloride ion diffusion coefficient, the experimental setup allows to measure chloride diffusion coefficient through nonsaturated concrete specimens with controlled degree of water saturated. The different degrees of water saturation of concrete specimens were obtained, by using saturated solutions of NaCl and KCl controlling the relative humidity, then applied Rapid Cloride Permeability Test method to measure the cloride diffusion coefficient. The test results show that chloride diffusion coefficient depends strongly on the degree of water saturation of concrete. Beside, this relationship shows the non-linear relationship, in which, chloride diffusion coefficient reachs the maximum value in fully saturated concrete specimens.

Abstract: A combined effect of moisture diffusion, heat transfer, and hygro-thermo-vapor pressure modeling for pre-mold QFN CMOS Image Sensor (CIS) package has been developed in this study. Hygroscopic swelling properties such as saturation, coefficient of moisture expansion (CME) and activation energy can be extracted through TMA (Thermal Mechanical Analysis) and TGA (Thermal Gravitational Analysis) instruments. Fick’s second law of transient diffusion is solved by using finite element analysis (FEA) to evaluate the overall moisture distributions. With obtained experimental data, a three-dimensional FEA CIS model using the “thermal-wetness” technique is developed to predict the moisture absorption, moisture desorption, temperature distributions, hygro-thermo-vapor pressure mechanical coupled effect and the residual stress distributions at JEDEC pre-conditioning standard JESD22-A120.

Abstract: In the present work, a kinetic study based on a diffusion model was performed by use of both kinetics and thermodynamic data as input parameters, it was possible to evaluate the kinetic constant at each phase interface for a biphase configuration FeB and Fe2B grown over the surfaces of Armco Fe and Fe-Cr binary alloys at 0.5 and 4wt. %Cr by powder- pack boriding. The simulated values of the kinetics constants by the model were compared to those found in the literature and a good agreement was observed. For the Fe-4wt. %Cr alloy, it was found by simulation that the layer thickness ratio between the FeB and Fe2B phases is very sensitive to the increase of temperature and surface boron content.

Abstract: Osmotic dehydration of pumpkin (Cucurbita pepo, L.) fruits was carried out with binary solutions of sucrose and NaCl at different temperatures and solute concentrations. Water loss and solids gain kinetics were experimentally determined and fitted using a diffusional model. Pumpkins samples were considered as finite cylinders and the analytical solution of the unsteady diffusion equation was used considering the external resistance to the mass transfer negligible. The influence of shrinkage and temperature on the effective diffusion coefficients was also assessed in this work.

Abstract: Fisher’s model for grain boundary diffusion considers the lattice and the grain boundary on the same basis by presuming the validity of Fick’s second law for both cases, despite the significant structural differences between them. Recent studies [1-3] have, however, shown that grain boundary diffusion is profoundly different from lattice diffusion. We propose an alternative mathematical formulation that incorporates these structural differences and consequently models grain boundary diffusion phenomena more accurately than Fisher’s model. This is achieved by considering possible deviations from the classical random walk for solute atoms diffusing through grain boundaries. This formalism can also be applied to surface diffusion and triple junction diffusion.

Abstract: A numerical approach for the segregation of atomic oxygen at Ag/MgO interfaces is presented. A general segregation kinetics is considered and the coupled system of differ- ential equations is solved due to a one-dimensional finite difference scheme which accounts for concentration-dependent diffusion coefficients. Based on a model oxide distribution, the influence of the concentration-dependency is numerically investigated and compared with the solution for constant coefficients. In addition, the numerical approach allows for the consider- ation of general boundary conditions, specimen sizes and time-dependent material and process parameters.

Abstract: In this work, an approach of reactive nitrogen diffusion is presented and applied to the iron gas nitriding process. A kinetic model based on Fick's laws is used to simulate the layer growth kinetics of a biphase configuration composed of ε and γ’ iron nitrides grown on the pure iron substrate. This diffusional approach, under certain assumptions, reveals the influence of the nitriding potential on the layer growth kinetics during the gas nitriding of pure iron. Some simulation results are presented and discussed.

Abstract: A numerical approach for the segregation of atomic oxygen at Ag/MgO interfaces is presented. A general segregation kinetics is considered and the coupled system of partial differential equations is solved due to a one-dimensional finite difference scheme. Based on a model oxide distribution, the influence of the oxide distribution is numerically investigated and compared with the solution for equidistant arrangements. The numerical approach allows for the consideration of general boundary conditions, specimen sizes and time-dependent material and process parameters. Furthermore, a numerical procedure to convert two-dimensional microstructures into representative one-dimensional distributions is described.

Abstract: In this work we develop an analytical method for resolution of the reaction-diffusion equations which govern impurity diffusion by the dissociative mechanism in a finite-thickness sample and from a deposit of solute atoms on the surface. This method is based upon the perturbation of basic solutions corresponding to limiting cases and the choice of suitable small parameters. The solutions obtained and their comparison to those of numerical studies are also presented in this paper.