Thermoelectric magnetohydrodynamic effects on the crystal growth rate of undercooled Ni dendrites

Thermoelectric magnetohydrodynamic control of melt pool dynamics and microstructure evolution in additive manufacturing

Large thermal gradients in the melt pool from rapid heating followed by rapid cooling in metal additive manufacturing generate large thermoelectric currents. Applying an external magnetic field to the process introduces fluid flow through thermoelectric magnetohydrodynamics. Convective transport of heat and mass can then modify the melt pool dynamics and alter microstructural evolution. As a novel technique, this shows great promise in controlling the process to improve quality and mitigate defect formation. However, there is very little knowledge within the scientific community on the fundamental principles of this physical phenomenon to support practical implementation. To address this multi-physics problem that couples the key phenomena of melting/solidification, electromagnetism, hydrodynamics, heat and mass transport, the lattice Boltzmann method for fluid dynamics was combined with a purpose-built code addressing solidification modelling and electromagnetics. The theoretical study presented here investigates the hydrodynamic mechanisms introduced by the magnetic field. The resulting steady-state solutions of modified melt pool shapes and thermal fields are then used to predict the microstructure evolution using a cellular automata-based grain growth model. The results clearly demonstrate that the hydrodynamic mechanisms and, therefore, microstructure characteristics are strongly dependent on magnetic field orientation. This article is part of the theme issue 'Patterns in soft and biological matters'.

Liquid phase separation in undercooled Cu-Co alloys under the influence of static magnetic fields

Undercooling of Cu-based alloys often induces metastable liquid phase separation followed by rapid solidification of separated liquids. The rapid solidification can help freeze in the morphology of a higher-melting liquid and eases difficulties in studies of liquid phase separation kinetics. In the present work, the influence of static magnetic fields on liquid phase separation in bulk Cu₈₄Co₁₆ composition was investigated. Inductively melted samples were glass-fluxed, undercooled and solidified under uniform and non-uniform magnetic fields generated by a superconducting magnet. Solidification microstructure of the phase-separated samples was examined using an optical microscope. The imposition of the magnetic fields, both uniform and non-uniform, altered the morphology, segregation pattern and size distribution of Co-rich droplets due to liquid phase separation. The imposition of the non-uniform magnetic fields with positive and negative gradients brought about segregation of the Co-rich droplets at the top and the bottom side of the samples, respectively. Such influence of the static magnetic fields is interpreted by assuming intensification of convective flow and Kelvin force-controlled migration of the Co-rich droplets. This article is part of the theme issue 'Heterogeneous materials: metastable and non-ergodic internal structures'.

From atomistic interfaces to dendritic patterns

Transport processes around phase interfaces, together with thermodynamic properties and kinetic phenomena, control the formation of dendritic patterns. Using the thermodynamic and kinetic data of phase interfaces obtained on the atomic scale, one can analyse the formation of a single dendrite and the growth of a dendritic ensemble. This is the result of recent progress in theoretical methods and computational algorithms calculated using powerful computer clusters. Great benefits can be attained from the development of micro-, meso- and macro-levels of analysis when investigating the dynamics of interfaces, interpreting experimental data and designing the macrostructure of samples. The review and research articles in this theme issue cover the spectrum of scales (from nano- to macro-length scales) in order to exhibit recently developing trends in the theoretical analysis and computational modelling of dendrite pattern formation. Atomistic modelling, the flow effect on interface dynamics, the transition from diffusion-limited to thermally controlled growth existing at a considerable driving force, two-phase (mushy) layer formation, the growth of eutectic dendrites, the formation of a secondary dendritic network due to coalescence, computational methods, including boundary integral and phase-field methods, and experimental tests for theoretical models-all these themes are highlighted in the present issue.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.

The boundary integral theory for slow and rapid curved solid/liquid interfaces propagating into binary systems

The boundary integral method for propagating solid/liquid interfaces is detailed with allowance for the thermo-solutal Stefan-type models. Two types of mass transfer mechanisms corresponding to the local equilibrium (parabolic-type equation) and local non-equilibrium (hyperbolic-type equation) solidification conditions are considered. A unified integro-differential equation for the curved interface is derived. This equation contains the steady-state conditions of solidification as a special case. The boundary integral analysis demonstrates how to derive the quasi-stationary Ivantsov and Horvay-Cahn solutions that, respectively, define the paraboloidal and elliptical crystal shapes. In the limit of highest Péclet numbers, these quasi-stationary solutions describe the shape of the area around the dendritic tip in the form of a smooth sphere in the isotropic case and a deformed sphere along the directions of anisotropy strength in the anisotropic case. A thermo-solutal selection criterion of the quasi-stationary growth mode of dendrites which includes arbitrary Péclet numbers is obtained. To demonstrate the selection of patterns, computational modelling of the quasi-stationary growth of crystals in a binary mixture is carried out. The modelling makes it possible to obtain selected structures in the form of dendritic, fractal or planar crystals.This article is part of the theme issue 'From atomistic interfaces to dendritic patterns'.