Anisotropic solid–liquid interface kinetics in silicon: an atomistically informed phase-field model

Abstract

We present an atomistically informed parametrization of a phase-field model for describing the anisotropic mobility of liquid–solid interfaces in silicon. The model is derived from a consistent set of atomistic data and thus allows to directly link molecular dynamics and phase field simulations. Expressions for the free energy density, the interfacial energy and the temperature and orientation dependent interface mobility are systematically fitted to data from molecular dynamics simulations based on the Stillinger–Weber interatomic potential. The temperature-dependent interface velocity follows a Vogel–Fulcher type behavior and allows to properly account for the dynamics in the undercooled melt.

Kinetics of solid–liquid interface motion in molecular dynamics and phase-field models: crystallization of chromium and silicon

“…The temperature dependences of the crystal–liquid interface velocity obtained in this work for Cr and Si are consistent with the results of earlier MD simulations, where a gradual decrease of the velocity from the maximum value down to zero is reported for most of the bcc metals [7,12,13,16] and Si [14,15].…”

“…Kinetics of solid-liquid interface in metals and alloys was widely investigated experimentally [1][2][3][4][5], in molecular dynamics (MD) simulations [2,[6][7][8][9][10][11][12][13][14][15][16], and theoretically, with the diffusionlimited theory (DLT) [17,18] and the collision-limited theory (CLT) [19,20]. Special attention has been devoted to the nonlinear [21] and often non-monotonous [2,[6][7][8][9][10][11][12][13][14][15][16] temperature dependence of the crystal growth velocity during rapid solidification, which manifests itself at high thermodynamic driving force for the phase transformation [22][23][24]. It has been shown [25] that the traditional kinetic theories, such as CLT and DLT, as well as the phase-field models (PFMs) based on local thermodynamic equilibrium [26], often fail to quantitatively describe the nonlinear behaviour in the crystal growth velocity predicted in MD simulations.…”

“…It has been shown [25] that the traditional kinetic theories, such as CLT and DLT, as well as the phase-field models (PFMs) based on local thermodynamic equilibrium [26], often fail to quantitatively describe the nonlinear behaviour in the crystal growth velocity predicted in MD simulations. While the local equilibrium PFMs can describe the nonlinear dependence of the interface velocity predicted in MD simulations in a relatively narrow temperature range [27], the extension of this description to a wider range of undercoolings, where the velocity goes through the maximum and slows down with increasing undercooling [2,[7][8][9][10][11][12][13][14][15][16], still presents a challenge.…”

Generation and Annealing of Crystalline Disorder in Laser Processing of Silicon

“…As shown in Fig. 10c, the velocities of the crystal-liquid interface with different crystallographic orientations are evaluated from a series of crystal-liquid coexistence simulations performed at different temperatures (Bergmann et al 2017). The {111} interface has the smallest velocity compared to the other two orientations, which is related to its densely packed structure and absence of favorable sites for the attachment of additional atoms on a {111} crystal face.…”

On jump relations of anisotropic elliptic interface problems

“…The above jump conditions are often referred as internal boundary conditions that make the problem well-posed. There are many discussions in the literature about anisotropic interface problems including physics and modeling [2,8,10], analysis [11,6,12], and numerical methods [4,1,5].…”