Local atomic order in the melt and solid-liquid interface effect on the growth kinetics in a metallic alloy model.

We illustrate for a solid-liquid interface how local atomic order in a metallic melt (NiZr) transforms into a massive in-plane ordering at the surface of a crystal (bcc Zr) when commensurability is given between the solute-centered clusters of the melt and the periodic potential of the crystalline surface for a given orientation. Linking molecular dynamics simulation to phase-field modeling allows us to estimate quantitatively the influence of the surface effect on the growth kinetics. This study sheds new light on the relation between the undercooling ability (e.g., in the case of glass-forming alloys) and the pronounced local order in the melt.

Spinodal decomposition and droplets entrapment in monotectic solidification.

In this article, we present two models to simulate solidification morphologies in monotectic alloys. With the first model, we investigate the morphological evolution under the influence of spinodal decomposition. The model requires that a gradient energy contribution for the concentration field should be incorporated, in order to stabilize phase separation when the liquid concentration is inside the region of miscibility gap. The free energy of the system in this model is derived from direct interpolation of the bulk energy densities. This, however, results in simulation regions in nanometer scale due to contributions from the chemical free energy of the system to the total surface excess. With the second model, our purpose is to develop a phase-field model to simulate scales that are larger than nanometer, where the departures from equilibrium are very small resulting in phase concentrations outside the spinodal region. In view of this, we exclude the concentration gradient contribution to the grand chemical potential functional, and develop a model based on [M. Plapp, Phys. Rev. E 84, 031601 (2011); A. Choudhury and B. Nestler, Phys. Rev. E 85, 021602 (2012)]. The advantage is that the free energy excess across the interface at equilibrium disappears, and hence it is easier to derive the required surface energies with higher interface widths. Due to this benefit, we employ the method to simulate the dynamic entrapment process in the monotectic reaction and study the influence of liquid(1) - liquid(2) surface energy and undercooling on the entrapment process.

Interface tracking characteristics of color-gradient lattice Boltzmann model for immiscible fluids.

We study the interface tracking characteristics of a color-gradient-based lattice Boltzmann model for immiscible flows. Investigation of the local density change in one of the fluid phases, via a Taylor series expansion of the recursive lattice Boltzmann equation, leads to the evolution equation of the order parameter that differentiates the fluids. It turns out that this interface evolution follows a conservative Allen-Cahn equation with a mobility which is independent of the fluid viscosities and surface tension. The mobility of the interface, which solely depends upon lattice speed of sound, can have a crucial effect on the physical dynamics of the interface. Further, we find that, when the equivalent lattice weights inside the segregation operator are modified, the resulting differential operators have a discretization error that is anisotropic to the leading order. As a consequence, the discretization errors in the segregation operator, which ensures a finite interface width, can act as a source of the spurious currents. These findings are supported with the help of numerical simulations.

Phase field modeling of fracture and stress-induced phase transitions.

We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the late stage of the Asaro-Tiller-Grinfeld instability. Starting from a sharp interface formulation we derive the elastic equations and the dissipative interface kinetics. We develop a phase field model to simulate these processes numerically; in the sharp interface limit, it reproduces the desired equations of motion and boundary conditions. We perform large scale simulations of fracture processes to eliminate finite-size effects and compare the results to a recently developed sharp interface method. Details of the numerical simulations are explained, and the generalization to multiphase simulations is presented.

Effect of solutal Marangoni convection on motion, coarsening, and coalescence of droplets in a monotectic system.

In this paper, we study the effect of solutal Marangoni convection (SMC) on the microstructure evolution in a monotectic system, using the convective Cahn-Hilliard and Navier-Stokes equations with a capillary tensor contributed by the chemical concentration gradient. At first, we simulate the spontaneous motion of two distant droplets induced by SMC and compare our results with an analytical solution. We then compute the coalescence of two droplets in contact and coarsening of two distant droplets considering different sizes. We further study the influence of SMC on the evolution of phase separation processes inside the spinodal region for Fe-50 at %Sn and Fe-40 at %Sn alloys. In the former case, we rationalize our results using Fourier spectra and in the latter case, we compare the size distribution of droplets with the LSW theory.

Description of hard-sphere crystals and crystal-fluid interfaces: a comparison between density functional approaches and a phase-field crystal model.

In materials science the phase-field crystal approach has become popular to model crystallization processes. Phase-field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic description of the system in question. We present a study on classical density functional theory in three stages of approximation leading to a specific phase-field crystal model, and we discuss the limits of applicability of the models that result from these approximations. As a test system we have chosen the three-dimensional suspension of monodisperse hard spheres. The levels of density functional theory that we discuss are fundamental measure theory, a second-order Taylor expansion thereof, and a minimal phase-field crystal model. We have computed coexistence densities, vacancy concentrations in the crystalline phase, interfacial tensions, and interfacial order parameter profiles, and we compare these quantities to simulation results. We also suggest a procedure to fit the free parameters of the phase-field crystal model. Thereby it turns out that the order parameter of the phase-field crystal model is more consistent with a smeared density field (shifted and rescaled) than with the shifted and rescaled density itself. In brief, we conclude that fundamental measure theory is very accurate and can serve as a benchmark for the other theories. Taylor expansion strongly affects free energies, surface tensions, and vacancy concentrations. Furthermore it is phenomenologically misleading to interpret the phase-field crystal model as stemming directly from Taylor-expanded density functional theory.

Phase-field simulations of nuclei and early stage solidification microstructures.

To investigate the local properties of heterogeneous nuclei on substrates, a phase-field model is extended to incorporate volume constraints and a third order line tension in the gradient free energy density formulation. The new model is applied to sessile drop simulations of Cu nuclei on Ni substrates to precisely analyse 3D equilibrium shapes and diffusion processes across the phase boundaries. In particular, the formalism with higher order potentials is used to investigate the length-scale dependent effect of the line tension on Young's force balance at triple lines in 3D. The employment of parallel and adaptive simulation techniques is essential for three-dimensional numerical computations. Early stage solidification microstructures of cubic Ni crystals are simulated by scale-bridging molecular dynamics (MD) and phase-field (PF) simulations. The domain of the PF computations is initialized by transferring MD data of the atomic positions and of the shape of the nuclei. The combined approach can be used to study the responses of microstructures upon nucleation.