•Rc calculated by TTT curve is taken as the intrinsic criteria to reflect the GFA.•TTT curve is plotted based on the isothermal phase field method.•Activation energy E has litter influence on the TTT curve and Rc.•Thermal activation energy Q controls nose tip and higher Q cannot get good C shape.•Results verify the glass prediction and experimental guidance by PFM.The critical cooling rate (Rc) calculated on the basis of the time-temperature-transformation (TTT) curve was taken as the intrinsic criteria of reflecting the glass forming ability (GFA) for the amorphous alloy. The TTT curves were plotted based on the isothermal Wheeler-Boettinger-McFadden (WBM) phase field method (PFM). By analyzing the TTT curves, the influence of different activation energy parameters E and Q for the interface mobility M and nucleation rate P respectively on Rc and GFA were investigated for Fe-25%B (mole fraction) binary amorphous alloy in present paper. The results showed that the activation energy E for the interface mobility M had litter influence on the nose temperature and time for the TTT curves. Under the different thermal activation energy Q1, Q2 and Q3 for the nucleation rate P, the temperatures and times corresponding to the nose tip were 500 K, 600 K, 775 K and 6.2 × 10− 4 s, 4.5 × 10− 4 s, 9.5 × 10− 4 s, respectively, and the calculated values of Rc were 1.57 × 106 K/s, 1.93 × 106 K/s, 7.35 × 105 K/s, respectively, which were in the range of 6.4 × 105 ~ 6.8 × 106 K/s from the experimental measurements. Under the influence of thermal activation energy Q, the nose tip temperature increased, which meant Q controlled the nose tip temperature, while the higher Q would not get the perfect C shape. It was found that the values of Rc calculated based on the TTT curves by the PFM were in good agreement with the reported experimental values, which verified the feasibility of the glass prediction and the research of the intrinsic physical mechanism of the GFA by the PFM.

•Temperature fields can affect the dendrite morphology, solute field and tip velocity.•Under an applied temperature gradient, the dendrite with an anisotropic cone shape can be formed.•Influence of different temperature gradient on the dendrite growth and solute distribution is analyzed.•Simulation results can give an experimental guidance for direct casting field.Phase field method was employed to investigate the effect of the applied temperature gradient on the microstructure evolution for the binary Ni–Cu alloy during the solidification process. As a comparison group, the isothermal solidification and the non-isothermal solidification taking into account the effect of latent heat were simulated at the same time. Simulation results showed that temperature distribution could greatly influence dendrite morphology, concentration distribution and tip velocity. Under the applied temperature gradient, a cone shape of dendrite, instead of the normal dendrite with four symmetric arms, could be found easily. The growth rate of dendrite and the segregation of concentration field increased with the increasing temperature gradient. This model was able to give a clear outlook for the influence of temperature gradient on the dendrite morphology and help a better design for the microstructure control in the field of direct chill casting.