Diffusion in Advanced Materials and Processing

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Authors: Dezső L. Beke, Z. Erdélyi
Abstract: Growth kinetic is either diffusion or interface reaction controlled process, characterized by parabolic or linear relationships, respectively. The well known diffusion paradox, predicting infinitely fast diffusion kinetics at short times (distances) for diffusion control will be discussed and resolved, by showing that the diffusion permeability across the interface should be finite at the very beginning of the process. Thus one can arrive at an atomistic interpretation of the interface transfer coefficient, K, and at linear growth kinetics even if there is no extra potential barrier present at the interface, usually assumed in the interpretation of interface reaction control. It is also shown that this phenomenon is a typical nanoeffect: after a certain diffusion distance (lying between 0.01 and 300 nm, depending on the composition dependence of the diffusion coefficient) the finite permeability of the interface will not restrict the growth and normal diffusion control will be observed.
Authors: Alan F. Jankowski
Abstract: Thermal anneal treatments are used to identify the temperature range of the two dominant diffusion mechanisms – bulk and grain boundary. To assess the transition between mechanisms, the low temperature range for bulk diffusion is established utilizing the decay of static concentration waves in composition-modulated nanolaminates. These multilayered structures are synthesized using vapor deposition methods as thermal evaporation and magnetron sputtering. However, at low temperature the kinetics of grain-boundary diffusion are much faster than bulk diffusion. The synthesis of Au-Cu alloys (0-20 wt.% Cu) with grain sizes as small as 5 nm is accomplished using pulsed electro-deposition. Since the nanocrystalline grain structure is thermally unstable, these structures are ideal for measuring the kinetics of grain boundary diffusion as measured by coarsening of grain size with low temperature anneal treatments. A transition in the dominant mechanism for grain growth from grain boundary to bulk diffusion is found with an increase in temperature. The activation energy for bulk diffusion is found to be 1.8 eV·atom-1 whereas that for grain growth at low temperatures is only 0.2 eV·atom-1. The temperature for transitioning from the dominant mechanism of grain boundary to bulk diffusion is found to be 57% of the alloy melt temperature and is dependent on composition.
Authors: Irina V. Belova, Andreas Öchsner, Nilindu Muthubandara, Graeme E. Murch
Abstract: The presence of atomic oxygen at internal metal-ceramic oxide interfaces significantly affects the physical properties of the interfaces which in turn affects the bulk properties of the material. This problem is addressed for the model composite system Ag-MgO from a phenomenological point of view using a lattice-based Monte Carlo method and a finite element method extended with special user-subroutines. We simulate the time dependence of oxygen depth and contour profiles. We are able to show very good agreement between these two methods.
Authors: Alexander V. Evteev, Elena V. Levchenko, Irina V. Belova, Graeme E. Murch
Abstract: The shrinkage via the vacancy mechanism of a mono–atomic nanotube is described. Using Gibbs–Thomson boundary conditions an exact solution is obtained of the kinetic equation in quasi steady–state at the linear approximation. A collapse time as a function of the size of a nanotube is determined. Kinetic Monte Carlo simulation is used to test the analytical analysis.
Authors: N.S. Raghavan, A.H. King
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.
Authors: Kwai S. Chan, Yi Ming Pan, Yi Der Lee
Abstract: First–principle computational methods have been utilized to compute the diffusion mobility of Mo, Cr, Fe, and W. A local density-based full-potential linearized augmented plane wave (FLAPW) code, named WIEN2K, was utilized to compute the electronic structure and total energy of an n-atom supercell with atom positions designed to simulate the desired diffusion processes. The computational procedure involves the calculations of the energy for vacancy formation and the energy barrier for solute migration in the host metal. First-principles computational results of the energy of vacancy formation, solute migration energy, activation energy for self-diffusion, as well as diffusion of Mo, Cr, Fe, and W solutes in Ni and vice versa are presented and compared against experimental data from the literature.
Authors: Kevin M. Day, Mysore A. Dayananda
Abstract: Selected diffusion couples investigated in the Cu-based and Fe-based multicomponent systems are examined for diffusion path development, zero-flux planes, uphill diffusion, and internal constraints for diffusion paths. The couples are analyzed for interdiffusion fluxes and interdiffusion coefficients with the aid of the “MultiDiFlux” program. Eigenvalues and eigenvectors are also determined from the interdiffusion coefficients determined over various ranges of composition in the diffusion zone. Slopes of diffusion paths at selected sections, including the path ends, are related to interdiffusion coefficients, interdiffusion fluxes and/or eigenvectors. These relations are explored with selected single phase diffusion couples in the Cu-Ni-Zn and Fe-Ni-Al systems and the calculated path slopes are compared with those directly determined from the concentration profiles. Relations between the gradient of interdiffusion flux and the concentration gradient are examined for each component in a two-phase Cu-Ni-Zn diffusion couple. The research is supported by the National Science Foundation.
Authors: Axel Griesche, M.P. Macht, Günter Frohberg
Abstract: We present diffusion measurements in metallic melts measured by capillary techniques and results of molecular dynamic simulations. The investigated systems are the binary alloy AlNi20 and the multicomponent bulk glass-forming alloy Pd43Cu27Ni10P20. The temperature range of interest reached from the glassy state to the equilibrium melt. In the glassy as well as in the deeply supercooled state, below the critical temperature Tc of the mode-coupling, theory (MCT), diffusion is a highly collective atomic hopping process. Both investigated systems show around Tc a change in the diffusion mechanism. Above the liquidus temperature, diffusion in Pd43Cu27Ni10P20 is a collective process whereas in AlNi20 the atoms diffuse probably by uncorrelated binary collisions. The influence of thermodynamic forces on diffusion in the liquid state of AlNi20 can be described by the Darken equation with an additional temperature independent correction factor (“Manning”- factor).

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