Instability of a binary eutectic solidification front to morphological perturbations due to rejection of a ternary impurity leads to the formation of eutectic colonies. Whereas, the instability dynamics and the resultant microstructural features are reasonably well understood for isotropic systems, several experimental observations point to the existence of colonies in systems with anisotropic interfaces. In this study, we extend the understanding of eutectic colonies to anisotropic systems, where certain orientations of the solid-liquid or solid-solid interfaces are associated with a lower free energy than the others. Through phase field simulations in 2D and 3D, we have systematically probed the colony formation dynamics and the resulting microstructures, as functions of the pulling velocity and the relative orientation of the equilibrium interfaces with that of the imposed temperature gradient. We find that in 2D, stabler finger spacings are selected with an increase in the magnitude of anisotropy introduced, either in the solid-liquid or in the solid-solid interface. The fingers have a well-defined orientation for the case of anisotropy in the solid-liquid interface, with no fixed orientations for the lamellae constituting the colony. For the case where anisotropy exists in the solid-solid interface, the lamellae tend to orient themselves along the direction of the imposed temperature gradient, with tilted solid-liquid interfaces from the horizontal. The 3D simulations reveal existence of eutectic spirals which might become tilted under certain orientations of the equilibrium interfaces. Our simulations are able to explain several key features observed in our experimental studies of solidification in Ni-Al-Zr alloy.

We use extended Cahn-Hilliard (ECH) equations to study faceted precipitate morphologies; specifically, we obtain four sided precipitates (in 2-D) and dodecahedron (in 3-D) in a system with cubic anisotropy, and, six-sided precipitates (in 2-D, in the basal plane), hexagonal dipyramids and hexagonal prisms (in 3-D) in systems with hexagonal anisotropy. Our listing of these ECH equations is fairly comprehensive and complete (upto sixth rank tensor terms of the Taylor expansion of the free energy). We also show how the parameters that enter the model are to be obtained if either the interfacial energy anisotropy or the equilibrium morphology of the precipitate is known. IntroductionProperties of crystalline materials are anisotropic due to the anistropy of the underlying continuum. In particular, the interfacial energy in crystalline systems is anisotropic and can have a strong influence on the formation and evolution of microstructures. Phase field models, which are best suited for the study of the formation and evolution of microstructures (see [1,2,3,4,5] for some recent reviews), have been used quite successfully to study the effect of interfacial energy anisotropy on microstructures and their evolution: see ] for some representative examples.The phase field models that incorporate interfacial energy anisotropy do so in one of two ways: (A) replace the gradient energy coefficient by an anisotropic function or polynomial, and (B) include higher order terms in the Taylor series expansion of the free energy functional. In this paper, we take the second approach -which is an extension of the original Cahn-Hilliard equation along the lines shown by Abinandanan and Haider [6] (hereafter referred to as ECHAH) and Torabi and Lowengrub [7] (hereafter referred to as ECHTL); this approach is argued to be advantageous in terms of the levels of anisotropy one can incorporate [6] and the kinetics remaining diffusionlimited [13]; in addition, the first method requires regularisation [22] for large anisotropies while ours does not.During solid-solid phase transformations interfacial energy anisotropy is known to lead to faceted precipitates: see for example, PbS precipitates in Na-doped PbTe system [31], Al 3 Sc precipitates in Al(Sc) alloys [32], Pt precipitates in sapphire [33], several metallic precipitates in internally reduced oxides [34], and Al 3 Ti precipitates in Al [35]. Our objective in this paper is to obtain, using phase field modelling, faceted precipitates in cubic systems that distinguish between 100 and 111 (for which one has to necessarily include fourth rank tensor terms [6]) and those that prefer 110 over both 100 and 111 (for which one has to necessarily include sixth rank tensor terms [8]); additionally, the sixth rank tensor terms can also be used to study

A straight-forward extension of the Jackson-Hunt theory for directionally solidifying multi-phase growth where the number of components exceeds the number of solid phases becomes difficult on account of the absence of the required number of equations to determine the boundary layer compositions ahead of the interface. In this paper, we therefore revisit the Jackson-Hunt(JH) type calculations for any given situation of multi-phase growth in a multi-component system and self-consistently derive the variations of the compositions of the solid phases as well as their volume fractions, which grow such that the composite solid-liquid interface is isothermal. This allows us to unify the (JH) calculation schemes for both in-variant as well as multi-variant eutectic reactions. The derived analytical expressions are then utilized to study the effect of dissimilar solute diffusivities and interfacial energies on the undercoolings and the solidified fractions.We also perform phase field simulations to confirm our theoretical predictions and find a good agreement between our analytical calculations and model predictions for model symmetric alloys as well as for a particular Ni-Al-Zr alloy.

Electroplasticity is defined as the reduction in flow stress of a material undergoing deformation on passing an electrical pulse through it. The lowering of flow stress during electrical pulsing has been attributed to a combination of three mechanisms: softening due to Joule-heating of the material, de-pinning of dislocations from paramagnetic obstacles, and the electron-wind force acting on dislocations. However, there is no consensus in literature regarding the relative magnitudes of the reductions in flow stress resulting from each of these mechanisms. In this paper, we extend a dislocation density based crystal plasticity model to incorporate the mechanisms of electroplasticity and perform simulations where a single electrical pulse is applied during compressive deformation of a polycrystalline FCC material with random texture. We analyze the reductions in flow stress to understand the relative importance of the different mechanisms of electroplasticity and delineate their dependencies on the various parameters related to electrical pulsing and dislocation motion. Our study establishes that the reductions in flow stress are largely due to the mechanisms of de-pinning of dislocations from paramagnetic obstacles and Joule-heating, with their relative dominance determined by the specific choice of crystal plasticity parameters corresponding to the particular material of interest. (Arka Lahiri), pratheek.shanthraj@manchester.ac.uk (Pratheek Shanthraj), f.roters@mpie.de (Franz Roters) not only during the pulses but also between the pulses [2-4]. Thus, repeated electropulsing during deformation mimics the attributes of hot working, albeit at a much lower energy cost. This has prompted development of industrial manufacturing paradigms like Electrically-assisted manufacturing (EAM) and Electroplastic manufacturing processing (EPMP) which leverage the phenomenon of EP on an industrial scale. There are several reviews of EAM, EPMP, and the phenomenon of EP which can serve as useful references in this regard [5-8].Even as there are increased efforts to harness the benefits of EP in the manufacturing industry, the mechanisms contributing to EP continue to be poorly understood. Researchers over the years have proposed several different theories to explain the reductions in flow stress during