Fig. 1 a SEM image and b XRD spectra of the as-quenched TB18 sample

Fig. 2 DSC and derivative (DDSC) curves of TB18 alloy showing the starting temperature and the finishing temperature of β → α phase transition with different heating rates. The latent heat (${\text{|}{{Q}}}_{\text{latent1}}\text{|}$ and ${\text{|}{{Q}}}_{\text{latent2}}\text{|}$) is calculated from the stating temperature to the finishing temperature: a from 40 ℃ to 900 ℃ at 10 ℃/min, b from 300 ℃ to 700 ℃ at 1 ℃/min

Fig. 3 Calculated α-transformed fraction as a function of the temperature using Eq. (1) during temperature range of phase transition for different heating rates. $ \xi _{\alpha } - T $ curve reflects the ratio of α-transformed fraction heating to a certain temperature during phase transition to that of the whole temperature range of phase transition

Fig. 4 Microstructures of TB18 alloy after continuous heating with different rates: a from 40 ℃ to 900 ℃ at 10 ℃/min showing the spot-like α precipitates in β matrix, b from 40 ℃ to 700 ℃ at 10 ℃/min showing the intragranular α, grain boundary α and precipitation zone form in β matrix, c from 40 ℃ to 300 ℃ at 10 ℃/min firstly and 300 ℃ to 700 ℃ at 1 ℃/min showing the short rod-like α distributes uniformly in β matrix

Fig. 5 a, b DSC curves of TB18 alloy and sapphire standard sample (α-Al2O3) with different heating rates, c, d specific heat capacity curves of TB18 alloy obtained by sapphire standard sample method and difference method with different heating rates, a, c from 40 ℃ to 900 ℃ at 10 ℃/min, b, d from 300 to 700 °C at 1 ℃/min

Fig. 6 Heat capacity variations (${{C}}_{\text{v}}$) of α and β in TB18 alloy at the phase transition range

Fig. 7 a Latent heat of phase transition(${{Q}}_{\text{latent}}$) as a function of α phase volume fraction, b the ratio of latent heat of phase transition ($|{{Q}}_{\text{latent}}|$) to endothermic heat (${{Q}}_{\text{endo}}$) as a function of α phase volume fraction

Fig. 8 Optical microscopy (OM) images showing the βt and precipitation free zone and TEM images showing the precipitation of α in βt zone with the final temperature of 450 ℃ (before phase transition), 550 ℃ (during phase transition) and 700 ℃ (after phase transition) at 10 ℃/min. The volume fraction of βt (f1), α in βt zone (f2), α (f) and α (fT) during heating are calculated

Fig. 9 OM images showing the βt and precipitation free zone and SEM images showing the precipitation of α in βt zone with the final temperature of 400 ℃ (before phase transition), 450 ℃ (during phase transition) at 1 ℃/min. Especially, α is distributed uniformly from the intra grain to the grain boundary with the final temperature of 700 ℃ (after phase transition) at 1 ℃/min. The volume fraction of βt (f1), α in βt zone (f2), α (f) and α (fT) during heating are calculated

Fig. 10 Magnification image of elliptical area in Fig. 7b showing the ratio of the latent heat of phase transition ($|{{Q}}_{\text{latent}}|$) to the endothermic heat (${{Q}}_{\text{endo}}$) calculated by α phase volume fraction