Denis Danilov

Phase-field modelling of solute trapping during rapid solidification of a Si–As alloy

Abstract The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid–liquid interface, a new definition of the nonequilibrium partition coefficient in the phase-field context is introduced. This definition leads, in particular for high growth velocities, to a better description of the available experimental data in comparison with other diffuse interface and sharp interface predictions.

Dendritic to globular morphology transition in ternary alloy solidification.

The evolution of solidification microstructures in ternary metallic alloys is investigated by adaptive finite element simulations of a general multicomponent phase-field model. A morphological transition from dendritic to globular growth is found by varying the alloy composition at a fixed undercooling. The dependence of the growth velocity and of the impurity segregation in the solid phase on the composition is analyzed and indicates a smooth type of transition between the dendritic and globular growth structures.

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 Youngs 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.

Atomistic and mesoscale simulations of free solidification in comparison

Solidification of an undercooled Lennard-Jones system is considered by atomistic and mesoscale simulations. The influence of the parameters of a Nose–Hoover thermostat on the temperature profile in the molecular dynamics box during the free solidification of the sample is analyzed. Direct comparison of the temperature profiles and of the interface dynamics in molecular dynamics with phase-field simulations is given.

Bridging the gap between molecular dynamics simulations and phase-field modelling: dynamics of a [NixZr1-x]liquid-Zrcrystal solidification front

Results are presented from phase-field modelling and molecular dynamics simulations concerning the relaxation dynamics in a finite-temperature two-phase crystal–liquid sample subjected to an abrupt temperature drop. Relaxation takes place by propagation of the solidification front under formation of a spatially varying concentration profile in the melt. The molecular dynamics simulations are carried out with an interatomic model appropriate for the NiZr alloy system and provide the thermophysical data required for setting up the phase-field simulations.Regarding the concentration profile and velocity of the solidification front, best agreement between the phase-field model and molecular dynamics simulation is obtained when increasing the apparent diffusion coefficients in the phase-field treatment by a factor of four against their molecular dynamics estimates.

Influence of the phase diagram on the diffuse interface thickness and on the microstructure formation in a phase-field model for binary alloy

A phase-field model is used to investigate the responses of planar interfaces and of eutectic microstructures on the different shapes of the phase diagram in binary alloy systems. Numerical solutions of the dynamic field equations show that the interfacial profile and the thickness of the diffuse boundary layer depend on the segregation of the alloy components. The simulations are presented for different openings of binary phase diagrams. A strong influence of the phase diagram on the evolution of eutectic microstructures is found and quantitatively evaluated by defining an appropriate measure. The results are interpreted in terms of weighting the different contributions in the phase-field equation.

PHASE-FIELD SIMULATIONS OF EUTECTIC SOLIDIFICATION USING AN ADAPTIVE FINITE ELEMENT METHOD

A finite element method with a semi-implicit time update and an adaptive mesh refinement is used to numerically simulate characteristic growth morphologies in binary eutectic alloys for varying process conditions. The evolution equations are based on a recently developed phase-field model.1 Microstructure formations in typical temperature-composition regions of the eutectic phase diagram are computed showing single cellular primary phase growth, melting of eutectics, eutectic and off-eutectic solidification. We consider 2D and 3D lamellar two-phase growths, analyze the angle conditions at the eutectic triple junctions for different surface entropy data and discuss the occurrence of wetting along the solid-solid interface.