## From Scripta

### November 28, 2010

Dai et al

We present a continuum model for the core relaxation of incoherent twin boundaries based on the Peierls–Nabarro framework, incorporating both the long-range strain field and the local atomic structure. The continuum model is applied to the finite size effect of twin boundaries and interactions of dislocations with twin boundaries. The obtained results agree well with the experimental and atomistic simulation results. This model provides a basis for quantitative study of structures and collective behaviors of twin boundaries within the continuum framework.

Aagesen et al

The evolution of the solid–liquid interface in an Al–Cu dendritic microstructure is predicted using a phase-field model and compared to experimental data. The interfacial velocities are measured during isothermal coarsening using in situ X-ray tomographic microscopy. Good qualitative agreement is found between experimental and simulated velocities. The diffusion coefficient of solute in the liquid is calculated by comparing the magnitude of velocities. The phase-field model is applicable to much larger physical systems than previously tested, increasing its utility for studying coarsening.

## From Acta

### November 28, 2010

Modelling of the influence of the vacancy source and sink activity and the stress state on diffusion in crystalline solids

Svoboda and Fischer

Diffusion in solids is a well-known phenomenon that has many consequences in technology and material science. Modelling of diffusion-controlled processes requires both a reliable theory of diffusion and reliable kinetic coefficients, as well as other thermodynamic data. Often the classical Darken theory, valid for stress-free systems with ideal vacancy source and sink activity, is generalized to multicomponent systems with ideal vacancy source and sink activity. Nazarov and Gurov presented a theory for stress-free systems with no vacancy source and sink activity. Recently we published a general theory of diffusion that accounted for the role of non-ideal vacancy source and sink activity, as well as the stress state. Since diffusion theories are tested and diffusion coefficients measured usually on diffusion couples, this paper presents evolution equations based on that general theory for a diffusion couple. In the limit, the equations of the Darken theory and the Nazarov and Gurov theory are valid for ideal vacancy source and sink activity and no vacancy source and sink activity, respectively. Simulations for binary and ternary diffusion couples demonstrate the influence of the vacancy source and sink activity and the stress state on evolution of site fraction profiles of components and vacancies, and on the Kirkendall effect.

Influence of anisotropy on heterogeneous nucleation

Mariaux and Rappaz

Heterogeneous nucleation is governed by the interplay of interfacial energies between a substrate, a solid and a liquid. Although the intensity of these energies can strongly change with the orientation of the nucleus for anisotropic media, this parameter is not taken into account in the available nucleation theories. In this paper, the Gibbs free energy barrier for nucleation is computed for an arbitrary solid–liquid interface energy. It is shown that anisotropy favors particular orientations of the nucleus on the substrate. Experimental evidence from the zinc–aluminum system is given as an application of this extended nucleation theory. It also sheds new light on the texture of galvanized steel sheets.

Serefoglu and Napolitano

The early-stage dynamics and onset mechanisms for eutectic solidification are investigated experimentally using slab-geometry slides of succinonitrile–(D)camphor (SCN–DC) transparent organic eutectic material. By specifically focusing separately on the pre-growth or holding period and the growth or pulling period, the critical roles of each in the establishment of initial conditions and the competition between eutectic initiation mechanisms, leading to the development of a steady-state eutectic front, are examined. It is found that a single-phase layer forms and increases in thickness monotonically with time during the holding period with a corresponding increase in the interface temperature. Because the thickness of this layer is observed to influence subsequent eutectic initiation mechanisms, it is concluded that the pre-existing structure, holding period duration, single-phase identity and thickness, and specimen slide geometry should all be reported as standard practice, along with the pulling velocity and thermal gradient, for a complete description of a gradient-zone directional solidification experiment.

Interaction between an edge dislocation and a circular inclusion with interface slip and diffusion

Wang and Pan

We investigate in detail the transient response induced by an edge dislocation near a circular elastic inclusion with simultaneous interface slip and diffusion. A rigorous solution to the interaction problem is derived in series form. As the time approaches infinity, our solution just recovers the classical one derived by Srolovitz et al. (Acta Metall 1984;32:1079) for fully relaxed boundary conditions. In addition, we observe that the edge dislocation will induce a uniform rigid-body rotation in the inclusion as the time approaches infinity. When the dislocation is far away from the inclusion, simple asymptotic expressions of the glide and climb forces on the dislocation are also obtained. Furthermore, five extreme cases for the imperfect interface are discussed; in particular, we derive approximate closed-form expressions of the decaying internal stress field within the inclusion and the image force on the dislocation for long-range stress relaxations when the interface diffusion occurs much faster than the interface slip and vice versa. Some interesting physical behaviors are observed.

## Papers from Acta

### November 15, 2010

N Moelans

The aimed properties of the interpolation functions used in quantitative phase-field models for two-phase systems do not extend to multi-phase systems. Therefore, a new type of interpolation functions is introduced that has a zero slope at the equilibrium values of the non-conserved field variables representing the different phases and allows for a thermodynamically consistent interpolation of the free energies. The interpolation functions are applicable for multi-phase-field and multi-order-parameter representations and can be combined with existing quantitative approaches for alloys. A model for polycrystalline, multi-component and multi-phase systems is formulated using the new interpolation functions that accounts in a straightforward way for composition-dependent expressions of the bulk Gibbs energies and diffusion mobilities, and interfacial free energies and mobilities. The numerical accuracy of the approach is analyzed for coarsening and diffusion-controlled parabolic growth in Cu–Sn systems as a function of R/ℓ, with R grain size and ℓ diffuse interface width.

[2] On the analytical solution for self-similar grain size distributions in two dimensions

C S Pande and K P Cooper

In a recent publication an analytical solution of the Fokker–Planck continuity equation for the grain size distribution for two-dimensional grain growth in the long time limit (self-similar state) was provided. It used von Neumann–Mullins law and the results of Rios and Glicksman, but was based on a stochastic formulation first proposed by Pande. In this paper this analytical solution is compared with experimental and computer simulation distributions. It is found that grain size distribution, as obtained by simulations of two-dimensional grain growth, although in agreement with our analytical results, may in fact differ from experimentally obtained grain size distributions in thin films. It is also shown mathematically that in the two limiting cases the general solution is reduced to the Hillert or Rayleigh distributions.

[3] Morphological evolution and growth mechanism of primary Mg2Si phase in Al–Mg2Si alloys

C Li et al

Three-dimensional morphologies of primary Mg2Si in Al–Mg2Si alloys were studied in detail using field emission scanning electron microscopy, and its growth mechanism was also discussed. Primary Mg2Si crystals in the alloys display various geometric shapes, such as octahedron, hopper, truncated octahedron, cube and enormous dendrite, although they tend to form faceted octahedron (equilibrium shape) with minimized total surface free energy. The higher growth rate along left angle bracket1 0 0right-pointing angle bracket induces the degradation of the six {1 0 0} facets to corners, while eight {1 1 1} facets remain to form octahedron Mg2Si because of their lower growth rates. However, the growth velocities of the left angle bracket1 0 0right-pointing angle bracket and left angle bracket1 1 1right-pointing angle bracket directions can be manipulated by means of external growth conditions, which are responsible for the evolution of Mg2Si crystals into other morphologies.

[4] Elongated nanoscale voids at deformed special grain boundary structures in nanocrystalline materials

I A Ovid’ko et al

A special micromechanism for the formation of elongated nanoscale voids at grain boundaries (GBs) in deformed nanocrystalline materials is suggested and theoretically described. Within our description, the formation of nanoscale voids represents a slow (diffusion-controlled) process driven by release of the elastic energy of GB disclination configurations formed due to GB sliding. It is demonstrated that the nucleation of elongated nanoscale voids at GB disclination dipoles occurs as an energetically favorable process in deformed nanocrystalline Ni and Al2O3 (sapphire) in wide ranges of their parameters.

T Fast et al

A novel mathematical framework called materials knowledge systems (MKS) was recently formulated to extract, store and recall computationally efficient hierarchical linkages that are at the core of multi-scale modeling of materials phenomena. A salient feature of this new framework is that it facilitates flow of high-fidelity information in both directions between the constituent length scales, and thereby offers a new strategy for concurrent multi-scale modeling. The viability of this new framework has thus far been largely explored for capturing the mechanical response of composite material systems. This paper extends the MKS framework to applications involving microstructure evolution, where the local states are typically defined in a continuous local state space. In particular, it will be shown that it is possible to obtain an efficient discretization of the local state space to produce a sufficiently accurate description of the linearized structure–structure evolution linkages for modeling spinodal decomposition. Furthermore, it will be shown that these linkages can be used successfully to accurately predict the continuous evolution of microstructure over the long time periods involved in such problems.