Understanding the formation of twinned dendrites (‘feather’ grains)

The phenomenon of feather grain growth is interesting from both a theoretical and commercial point of view. Here we report the results of phase-field simulations aimed at understanding the formation of twinned dendrites. We show that, while a competition between oppositely directed capillary and kinetic anisotropies with a simple four-fold symmetry can produce low anisotropy structures such as dendritic seaweed, there is no indication that this can give rise to twinned dendrites. In contrast, adding small components of an anisotropy, with higher order harmonics, can produce features reminiscent of twinned dendrites and may also be able to stabilise the grooved tip morphology

An adaptive, fully implicit multigrid phase-field model for the quantitative simulation of non-isothermal binary alloy solidification

Using state-of-the-art numerical techniques, such as mesh adaptivity, implicit time-stepping and a non-linear multi-grid solver, the phase-field equations for the non-isothermal solidification of a dilute binary alloy have been solved. Using the quantitative, thin-interface formulation of the problem we have found that at high Lewis number a minimum in the dendrite tip radius is predicted with increasing undercooling, as predicted by marginal stability theory. Over the dimensionless undercooling range 0.2–0.8 the radius selection parameter, σ*, was observed to vary by over a factor of 2 and in a non-monotonic fashion, despite the anisotropy strength being constant

Advanced numerical methods for the simulation of alloy solidification with high Lewis number

A fully-implicit numerical method based upon adaptively refined meshes for the thermal-solutal simulation of alloy solidification in 2D is presented. In addition we combine an unconditional stable second-order fully-implicit time discretisation scheme with variable step size control to obtain an adaptive time and space discretisation method, where a robust and fast multigrid solver for systems of non-linear algebraic equations is used to solve the intermediate approximations per time step. For the isothermal case, the superiority of this method, compared to widely used fully-explicit methods, with respect to CPU time and accuracy, has been demonstrated and published previously. Here, the new proposed method has been applied to the thermalsolutal case with high Lewis number, where stability issues and time step restrictions have been major constraints in previous research

Quantification of mesh induced anisotropy effects in the phase-field method.

Phase-field modelling is one of the most powerful techniques currently available for the simulation from first principles the time dependant evolution of complex solidification microstructures. However, unless care is taken the computational mesh used to solve the set of partial differential equations that result from the phase-field formulation of the solidification problem may introduce a stray, or implicit, anisotropy, which would be highly undesirable in quantitative calculations. In this paper we quantify this effect as a function of various computational parameters and subsequently suggest techniques for mitigating the effect of this stray anisotropy

The effect of the ratio of solid to liquid conductivity on the side-branching characteristics of dendrites within a phase-field model of solidification

We use a phase-field model of dendritic growth in a pure undercooled melt to examine the effect of the ratio of the thermal conductivities in the solid and liquid states (mu = ks/kl) on the side-branching characteristics of the dendrite. We find that high conductivity in the solid favours extensive side-branching while low conductivity in the solid appears to strongly suppress side branching. Over the range 0.5 < mu < 2.0, which is typical of most (metallic) systems which display dendritic growth the RMS distance at which the mean amplitude of the side-branches becomes equal to the tip radius varies from as little as 10 tip radii to in excess of 45 tip radii. This implies that there may be significant morphological difference between dendrites grown in different materials. The variation does not appear to follow exactly the analytical relationship predicted by solvability theory

Structure and phase-composition of Ti-doped gas atomized Raney-type Ni catalyst precursor alloys

Raney-type Ni precursor alloys containing 75 at.% Al and doped with 0, 0.75, 1.5 and 3.0 at.% Ti have been produced by a gas atomization process. The resulting powders have been classified by size fraction with subsequent investigation by powder XRD, SEM and EDX analysis. The undoped powders contain, as expected, the phases Ni2Al3, NiAl3 and an Al-eutectic. The Ti-doped powders contain an additional phase with the TiAl3 DO22 crystal structure. However, quantitative analysis of the XRD results indicate a far greater fraction of the TiAl3 phase is present than could be accounted for by a simple mass balance on Ti. This appears to be a (TixNi1-x)Al3 phase in which higher cooling rates favour small x (low Ti-site occupancy by Ti atoms). SEM and EDX analysis reveal that virtually all the available Ti is contained within the TiAl3 phase, with negligible Ti dissolved in either the Ni2Al3 or NiAl3 phases

Phase field analysis of eutectic breakdown.

In this paper an isotropic multi-phase-field model is extended to include the effects of anisotropy and the spontaneous nucleation of an absent phase. This model is derived and compared against a published single phase model. Results from this model are compared against results from other multi-phase models, additionally this model is used to examine the break down of a regular two dimensional eutectic into a single phase dendritic front

Three dimensional thermal-solute phase field simulation of binary alloy solidification

We employ adaptive mesh refinement, implicit time stepping, a nonlinear multigrid solver and parallel computation to solve a multi-scale, time dependent, three dimensional, nonlinear set of coupled partial differential equations for three scalar field variables. The mathematical model represents the non-isothermal solidification of a metal alloy into a melt substantially cooled below its freezing point at the microscale. Underlying physical molecular forces are captured at this scale by a specification of the energy field. The time rate of change of the temperature, alloy concentration and an order parameter to govern the state of the material (liquid or solid) are controlled by the diffusion parameters and variational derivatives of the energy functional. The physical problem is important to material scientists for the development of solid metal alloys and, hitherto, this fully coupled thermal problem has not been simulated in three dimensions, due to its computationally demanding nature. By bringing together state of the art numerical techniques this problem is now shown here to be tractable at appropriate resolution with relatively moderate computational resources

Estimation of cooling rates during close-coupled gas atomization using secondary dendrite arm spacing measurement

Al-4 wt pct Cu alloy has been gas atomized using a commercial close-coupled gas-atomization system. The resulting metal powders have been sieved into six size fractions, and the SDAS has been determined using electron microscopy. Cooling rates for the powders have been estimated using a range of published conversion factors for Al-Cu alloy, with reasonable agreement being found between sources. We find that cooling rates are very low relative to those often quoted for gas-atomized powders, of the order of 10 K s for sub-38 μm powders. We believe that a number of numerical studies of gas atomization have overestimated the cooling rate during solidification, probably as a consequence of overestimating the differential velocity between the gas and the particles. From the cooling rates measured in the current study, we estimate that such velocities are unlikely to exceed 20 m s