Fig. 1 a Aging-hardening curves of the alloys aged at 160 °C and 180 °C; b engineering stress-strain curves of the samples at peak-aged states indicated by the circles in a, respectively

Fig. 2 a, b HAADF-STEM images of the two peak-aged alloys in 160 °C-36 h and 180 °C-20 h states, respectively. The T1 and δ′/θ′/δ′ precipitates are indicated by green and orange arrows, respectively; c, d renderings of the 3DET reconstruction results of the microstructures in a, b. Rod-like Li-riched GPB zones are marked by the red ellipses

Fig. 3 Atomic-resolution HAADF-STEM images of a a single-layer thick T1 precipitate along a < 110 > zone axis, and c a typical δ′/θ′/δ′ composite precipitate along a < 100> zone axis; b a model describing the atomic arrangement of a sheared single-layer T1 precipitate. The atomic structure of T1 refers to literature [37] and the atomic structure of δ′/θ′/δ′ refers to studies [11,14]. The double-headed arrows indicate the created precipitate-matrix interfaces, and the zone (or thickness) of the precipitate is shown to include the adjacent Al atomic layers

Fig. 4 a Graphic illustration of the voxelization of the precipitates; b, c graphic illustration explaining the effective pixel size of the vertical precipitate in a along its broad surface

Fig. 5 Flow chart of the detection and measurement: a 2D sliced image from the 3DET volume; b, c Laplacian and Sobel filtered images of a; d map of marks produced by the feature-based detection algorithm; e measurement of string lengths in situ from locally filtered images; f map of marks after measurement; g refined map of marks

Fig. 6 Illustration diagram of the three feature detectors and the identification method

Fig. 7 3D renderings of the marks before a and after b refinement

Fig. 8 a, b Renderings of the 3DET reconstruction results of the two peak-aged alloys in 160 °C-36 h and 180 °C-20 h states; c, d renderings of the detected T1 precipitates (green) and δ′/θ′/δ′ composite precipitates (orange), respectively, on one habit plane from a, b

Fig. 9 a, b Histograms of the measuring errors of the feature-based detection algorithm of T1 and δ′/θ′/δ′. The errors were evaluated by manual comparison. c, d Two examples of large errors caused by image contrast interaction between the precipitates

Fig. 10 Comparison of the experimentally measured precipitation strengthening contribution with the plotting of the calculated precipitation strengthening contribution against γeff in a 160 °C–36 h state and b 180 °C–20 h state. Line A represents the predicted strengthening contribution of δ′/θ′/δ′ precipitates $\Delta \tau_{{\text{O}\{ 100\} }}^{{\delta^{\prime}/\theta^{\prime}/\delta^{\prime}}}$. Curve B represents the predicted precipitation strengthening contribution ∆τp as a function of γeff. Line C represents the experimentally measured precipitation strengthening contribution $\Delta \tau_{{\text{p}}}^{{{\text{Exp}}}}$