Table 1 Values of phase-field model parameters used in simulations

Grid size \(\Delta x\)

1

Time-step width \(\Delta t\)

0.07

Length scale parameter \(\varepsilon \)

6.5

Interfacial energy density \(\gamma _{\alpha \beta }\), i.e., \(\gamma _{g,g}\) and \(\gamma _{g,l}\)

1

Higher order parameter \(\gamma _{\alpha \beta \delta }\)

10

Kinetic coefficient for grain–grain interface \(\tau _{g,g}\)

100

Kinetic coefficient for grain–liquid interface \(\tau _{g,l}\)

1