Fig. 1 Schematic diagram of experimental apparatus for alloy solidification in an AMF

Fig. 2 One-dimensional domain for microsegregation model

Fig. 3 Morphologies of Al-4.5 wt%Cu alloy solidified at the cooling rate of 15 °C min-1 with different AMF intensities: a 0 T; b 0.05 T; c 0.1 T; d non-equilibrium lamellar eutectics under 0.1 T

Fig. 4 Amount of non-equilibrium eutectics in the solidified Al-4.5 wt%Cu alloy at various cooling rates with and without AMFs

Fig. 5 a SDAS plotted against the cubic root of solidification time, b coarsening coefficient in different AMF intensities and c amount of non-equilibrium eutectics calculated using measured coarsening coefficients. The following values are used for calculations: k0 = 0.14, Ceut = 33.2 wt% [33], \(D_{\text{s}} = 2.04 \times 10^{ - 5} \exp ( - 15336/T)\) m2 s-1 [34]

Fig. 6 a Calculative effective solid diffusion coefficient at 548 °C in AMFs. The following parameters are used: ρd0 = 1013 m-2, H0 = 0.1 T [43], r = 0.5 nm [44], \(D_{\text{eff}} (0) = 2.04 \times 10^{ - 5} \exp ( - \;15336 /T)\) m2 s-1 [34], \(D_{\text{d}} = 1.71 \times 10^{ - 4} \exp ( - \;9780.8 /T)\) m2 s-1 [44], \(D_{\text{L}} = 2 \times 10^{ - 6} \exp ( - \;17159.4 /T)\) m2 s-1 [45]; b calculated amount of non-equilibrium eutectics in consideration of the change in solid diffusivity in the AMF

Fig. 7 a Effective partition coefficients at different cooling rates with different AMFs, b concentration versus fraction solid profiles at the cooling rate of 15 °C min-1 with different AMFs

Fig. 8 Calculated and experimental results of amount of non-equilibrium eutectics with and without AMFs