Fig. 1. (a) Various sample geometries used in the experiments. Disk: DSC measurement. Platelet: hardness measurement and PALS. Meander: electrical resistivity measurement. (b) Schematic of heating device. (c) Experimental heating curves from room temperature ～20-400 °C. Inset: zoom-in of the initial temperature overshoots (arrows) deviating from perfect linear heating (broken lines). The axis labels and units for the inset are the same as for the main Fig. 1(c).

Fig. 2. Evolution of various properties during linear heating at (a) 3 K min-1 (b) 10 K min-1, (c) 50 K min-1. All are after solutionising and quenching. Precipitation stages are defined by vertical broken lines and numbered. Horizontal dotted lines represent the zero values of two of the observables. Different DSC peaks are denoted by letters a-c. Data delimited by the purple dotted line in stage 3 are further investigated in Fig. 5(b).

Fig. 3. (a-c) BF images of samples after linear heating to peak hardness, (a) 240 °C at 3 K min-1 (sample A), (b) 260 °C at 10 K min-1 (sample B), and (c) 280 °C at 50 K min-1 (sample C). (d) Representative HAADF image of a needle-shaped precipitate viewed along the needle axis. Red box marks the unit cell of the β″ structure. The lattice parameters a and c are measured after calibrating the drift distortion using the known Al lattice constant. Yellow arrows indicate the orientation relationships between the precipitate and the Al matrix. Inset shows the fast Fourier transform of the image. (e) Precipitate length distribution based on a statistics of ～150 precipitates in the three samples appearing in (a-c) (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

Fig. 4. Comparison of hardening caused by isothermal ageing and linear heating at (a) 3 K min-1, (b) 10 K min-1, (c) 50 K min-1. The isothermal ageing time was the same as the heating time to a given temperature, namely$t=\frac{T-{{20}^{\circ }}\text{C}}{\phi }$. Note that the ‘isothermal ageing’ curve does not represent a continuous heat treatment but a connection of individual hardnesses after isothermal ageing at various temperatures for various times.

Fig. 5. (a) Fitting of peak b in the DSC trace of 3 K min-1 (Fig. 2(a)) using one positive and one negative Gaussian function. (b) Electrical resistivity change as a function of DSC integral at the peak b. Data taken from the marked ranges in Fig. 2. Arrows point at the positions of the peak b. Dashed and dotted lines represent the two stages. For 50 K min-1, due to fluctuations of the resistivity data it is hard to determine two stages.

Fig. 6. Experimental DSC cluster peaks (a) and simulated cluster peaks in linear heating (b) using the model and parameters developed in Ref. [34]. Values below the peaks in (a) and beside the peaks in (b) denote the integrated peak areas.

Fig. 7. (a) Hardness plotted as a function of DSC integral for various heating rates. The red-shaded region is further replotted in (b) where the hardness increment relative to the state before linear heating is presented, featuring a linear relationship $\text{ }\!\!\Delta\!\!\text{ }\mathcal{H}\propto {{Q}_{\text{int}}}$. The green-shaded area in (a) represents a square root relationship$\text{ }\!\!\Delta\!\!\text{ }\mathcal{H}\propto \sqrt{{{Q}_{\text{int}}}}$. (b) also includes data of cluster hardening during linear heating at 10 K min-1 of samples after natural ageing (NA) for 1 h (Fig. S5).

Fig. 8. Representation of the phenomena occurring in Fig. 4 using the model and parameters in Ref. [34] to explain the role of excess vacancies during ageing. “Isothermal” at temperature T refers to ageing for a time t=T-20°Cϕ, corresponding to given reference heating rate ϕ.