Fig.1 Simulated morphologies of wollastonite at t=1 s for slag A at (a) 1320℃; (b) 1360℃ with anisotropy in the interface energy only (c) 1320℃ and (d) 1360℃ with anisotropy in interface energy and interface kinetics

Fig. 2 Simulated and experimental morphologies of wollastonite for different undercoolings for slag A: (a) ∆=65℃; (b) ∆=85℃; (c) ∆=105℃ after a simulation time of 1 s and (d) ∆=15℃; (e) ∆=35℃; (f) ∆=65℃ observed in the experiments

Fig. 3 Simulated and experimental morphologies of wollastonite for different undercoolings for slag B: (a) ∆=60℃; (b) ∆=80℃; (c) ∆=90℃ after a simulation time of 1 s and (d) ∆=0℃; (e) ∆=20℃; (f) ∆=40℃ observed in the experiments

Fig. 4 (a) The simulated dendrite in slag A at 1320℃ is presented by means of the 0.5 contour of ηliquid for different time steps, (b) dendrite tip position as a function of time. The dendrite tip velocity is determined as the slope of this line

Fig. 5 (a) Dendrite tip velocity and (b) radius of wollastonite dendrite as a function of the undercoolings. The data of phase field simulations (filled mark) are shown in comparison with experimental data (open mark)

Fig. 6 Products of dendrite tip velocity and radius as a function of the undercoolings. The data of phase field simulations are shown in comparison with experimental data and the solutions from the 2D and 3D Ivantsov relations. The ρv values obtained from the simulations for slag B overlap with those obtained from the 2D Ivanstov equation