Grain growth competition during thin-sample directional solidification of dendritic microstructures: A phase-field study

Abstract

We present the results of a comprehensive phase-field study of columnar grain growth competition in bicrystalline samples in two dimensions (2D) and in three dimensions (3D) for small sample thicknesses allowing a single row of dendrites to form. We focus on the selection of grain boundary (GB) orientation during directional solidification in the steady-state dendritic regime, and study its dependence upon the orientation of two competing grains. In 2D, we map the entire orientation range for both grains, performing several simulations for each configuration to account for the stochasticity of GB orientation selection and to assess the average GB behavior. We find that GB orientation selection depends strongly on whether the primary dendrite growth directions have lateral components (i.e. components perpendicular to the axis of the temperature gradient) that point in the same or opposite directions in the two grains. We identify a range of grain orientations in which grain selection follows the classical description of Walton and Chalmers. We also identify conditions that favor unusual overgrowth of favorably-oriented dendrites at a converging GB. We propose a simple analytical description that reproduces the average GB orientation selection from 2D simulations within statistical fluctuations of a few degrees. In 3D, we find a similar GB orientation selection as in 2D when secondary branches grow in planes parallel and perpendicular to the sample walls. Remarkably, quasi-2D behavior is also observed even when those perpendicular sidebranching planes are rotated by a finite azimuthal angle about the primary dendrite growth axis as long as the absolute values of those azimuthal angles are equal in both grains. In contrast, when the absolute values of those azimuthal angles differ markedly, we find that unusual overgrowth events at a converging GB are promoted by a high azimuthal angle in the least-favorably-oriented grain. We also find that diverging GBs can be strongly affected by those azimuthal angles, while converging GBs exhibit a weak dependence on those angles. For diverging GBs, GB orientation is also strongly affected by the relative signs of the lateral components of the primary dendrite growth directions in both grains.

Multiscale dendritic needle network model of alloy solidification with fluid flow

“…Such an extension would allow for mapping of entire ranges of crystalline orientations, as well as amplitudes and relative orientations of the temperature gradient and gravity. One could thus investigate the influence of these processing conditions upon the selection of inner grain spacings [18] and that of orientation and roughness of grain boundaries [88][89][90].…”

Comparative study of directional solidification of Al-7 wt% Si alloys in Space and on Earth: Effects of gravity on dendrite growth and Columnar-to-equiaxed transition

“…The growth competition of these two dendrites could be explained by the classical model proposed by Walton and Chalmers [55][56][57]. During the steady-state dendrite growth, grains at the solidification front should grow at the same velocity in the direction of the temperature gradient, so that v 1 = v 2 ' for the two dendrites in Fig.9.…”

Influence of morphological instability on grain boundary trajectory during directional solidification

“…Competition between grains of different orientations has been thoroughly studied for growth velocities well above the onset of morphological instability, in a regime where the solid-liquid interface is strongly morphologically unstable and forms dendritic array structures (see Refs. [6,7] and references therein). In this dendritic regime, grain boundaries meet the solid-liquid interface deep inside the semi-solid mushy zone (i.e.…”

“…In this dendritic regime, grain boundaries meet the solid-liquid interface deep inside the semi-solid mushy zone (i.e. far behind the dendrite tips) and have a negligible influence on grain selection, which is predominantly controlled by the growth competition of primary, secondary, and tertiary dendrite arms from neighboring grains at the leading edge of this zone [6,7].…”