Comparison of mechanical behavior

Figure 2 shows the effect of precipitates on compression in three types of nano-pillars (Ti-32Mo, ω iso -Ti-20Mo, and ω ath -Ti-1023 alloy), additional strain-stress curves are shown in Supplementary Fig. S2. The “jerkiness” of the strain-stress curve decreases from (a) to (b) at the large pillar sizes, while the reduction becomes not obvious at small pillar sizes. The “jerkiness” dramatically decreases in (c) at all pillar sizes. It indicates that ω iso can reduce the stress fluctuations at the large pillar sizes while the ω ath can reduce the stress fluctuations at all pillar sizes. It is noted that the stress-strain curves of the ω iso -Ti-20Mo alloy (Fig. 2b) show obvious stress oscillation, especially for 1.0 and 2.0 µm pillars, which is caused by the activation of large slip bands42. In contrast, the stress-strain curves of ω ath -Ti-1023 alloy (Fig. 2c) exhibit continuous stable plastic flow phenomenon. Thus, we simply calculate the slope of the curve at stress increasing region from 6% to 11% to represent the ω strengthening effect. The calculated slopes in ω iso -Ti-20Mo alloy are 6040 MPa for 2.0 µm pillar and 5308 MPa for 1.0 µm pillar, while the slopes in ω ath -Ti-1023 alloy are 3660 MPa for 2.0 µm pillar and 3886 MPa for1.0 µm pillars. The result shows that ω iso precipitate exhibit a higher strengthening effect and a less stable effect on plasticity than the ω ath precipitate. After deformation, multiple large slip bands were found after deformation in (a), (b), and many slip lines (but no slip bands) with small amplitudes occur on the pillar surface in (c). Only one slip system is activated when the samples are deformed in <011>. The slip planes have angles of ca.52° with the {011} top surface and represents the {112} <111> slip system.

Figure 2 Compression test on β-Ti alloy nano-pillars. (a–c) Comparison of mechanical behavior for the three scenarios in Fig. 1 and different pillar sizes. (d–f) The SEM images show the equivalent slip configurations for the three alloys of 2 μm pillars. Full size image

Statistics for stress drops and waiting times

The stress-strain curves in Fig. 2 were analysed by calculating the squared temporal derivatives of the stress: (dσ/dt)2 30,31,43. The detailed calculations are described in the section of statistics method and Supplementary Fig. S3. The avalanche statistics are shown for the three cases in Fig. 3a–c containing some very large events, which correspond to spanning slips, and a multitude of smaller events of dislocation glide. Only the latter are included in the probability distribution function (PDF) because the sizes of the largest stress drops are determined by boundary conditions (spanning avalanches from surface to surface). The PDFs are strongly size dependent and collapse onto a master curve when the amplitudes are normalized by the average amplitude for each system.

Figure 3 Probability distribution functions for stress drops and waiting times for the three scenarios in Fig. 2. (a–c) The stress drops are normalized by the average stress drop, which rescales all curves to be independent of the pillar diameter. The fitting line in (c) is cut-off power law P(s) = s−1.3exp(−s/2.68) ∗ (1 − exp(−s/15.64)). (d–f) The waiting times are normalized by the average waiting time, which rescales all curves to be independent of the pillar diameter. The fitting line in (f) is exponential distribution with P(s) = 0.29 ∗ exp(−s/s o ), where s o is normalized to 1.0. Full size image

Power law distributions were found only for the first two scenarios. The fitted power law exponents are almost identical: 1.96 and 2.05 with the incorporation of ω iso precipitates. A drastic change of the PDF occurs in the third scenario when ω ath precipitates are introduced. Crackling noise of stress drops (measured as normalized (dσ/dt)2) now follows a distribution P(s) = s−τexp(−s/s 1 )(1 − exp(−s/s 2 ))44 with τ = 1.3, s 1 = 2.68 and s 2 = 15.64 where the high energy cut-off s 1 dominates. Waiting time analysis shows the same sequence (Fig. 3d–f): the first two scenarios show power law distributed waiting times (normalized waiting time: waiting time/<waiting time>) with exponents 1.95 and 1.92. The third scenario yields an exponential distribution P(s) = 0.29 ∗ exp(−s/s o ) with s o normalized by the average waiting time. In the Supplementary Fig. S4, we show how the exponents are estimated by Maximum Likelihood method44,45 for stress drops and waiting times.

Deformation characterization

The deformation mechanisms of the three β-Ti alloy pillars are analysed by (scanning) transmission electron microscopy ((S)TEM). We observe that deformation of Ti-32Mo pillar is mediated by dislocation slip (Supplementary Fig. S5), which is typical for BCC alloys, and shows large avalanche amplitudes in stress-strain curves7,41. Precipitates hinder such dislocation movements in the slip plane of ω iso -Ti-20Mo pillars (Supplementary Fig. S6). Further loading increases the stress concentration in front of ω iso precipitate, and leads to dislocations cut through the precipitate42,46. The movement of dislocations is reduced and avalanche amplitudes are smaller than in the first scenario.

Rotations of ω ath precipitates occur in ω ath -Ti-1023 pillars under applied stress. TEM images of a ω ath -Ti-1023 pillar with 5% compressive strain show many parallel slip planes (Fig. 4a). Figure 4a is the enlarged view of the purple square area of the lower-right inset. It is clearly seen that the slip region in Fig. 4a stems from the deformed area. Selected area electron diffraction (SAED) of the non-slip region (blue rectangle in Fig. 4a) show that the diffraction intensities of two equivalent ω ath variants (ω ath1 and ω ath2 ) are almost identical. Dark-field TEM images using ω ath1 and ω ath2 reflections (Fig. 4b,c) further prove that the concentrations of ω ath1 and ω ath2 precipitates in the non-slip region are identical. The SAED patterns of the slip region show only a weak diffraction intensity of ω ath1 , and a strong diffraction intensity of ω ath2 (red rectangle in Fig. 4a). The related dark-field TEM images using ω ath1 and ω ath2 reflections (Fig. 4d,e) show that ω ath1 precipitates almost disappeared, while the number of ω ath2 approximately doubled. The absence of the ω ath1 inside slip planes indicates a transformation from ω ath1 to ω ath2 under stress. STEM annular bright-field (ABF) lattice images of the slip region (Fig. 4f) also show that ω ath1 variant rotate to ω ath2 variant. The ω ath phase is identified by the atomic structural feature, which is used in reference40. Typical ω ath2 crystal lattices are highlighted by six blue dots. There is no sharp boundary between β matrix and ω ath phase as the structural similarity and coherent nature of the interface. The blue ellipses in Fig. 4f are approximate indications of the ω ath2 phase boundaries. Along the slip direction, ω ath2 is preferred, while ω ath1 is not preferred from Fig. 4d,e. However, we do find that some ω ath1 structures (represented by six green spots) still exist in the ω ath2 phase region. As the average ω ath lattice parameter is 3.27 nm, the fact that ω ath2 and ω ath1 phase co-exist within 2 nm-region along the slip bands indicates some ω ath1 phase is not rotated and retains its previous orientation. The Burger’s vector orientation of most dislocations around ω ath precipitate are consistent with the slip direction (shown in Fig. 4f,g), while the orientation of dislocation (numbered 2) in front of ω ath precipitate derivate from the slip direction, where the dislocation is obstructed by the ω ath precipitate along its pathway. The accumulation of dislocations in front of ω ath precipitate will lead to an obvious lattice distortion and thus its Burger’s vector orientation is different from other dislocations. Therefore, the variant rotation is activated by stress concentration of dislocation pile-ups in front of ω ath inclusions, and then facilitates the nucleation of new dislocations (indicated by blue dotted boxes in Fig. 4f). The propagation of dislocations is now blocked and restarts on the other side of the rotated ω ath variant (or other sites where the stress concentration is high) with further loading, leading to many tiny slip lines, but no big slip bands.

Figure 4 Deformation features of ω ath -Ti-1023 pillars with 5% compression strain. (a) Bright-field image of deformed pillar with many slip lines, which is the enlarged view of the purple square area of the lower-right inset containing the whole slip region. The blue and red rectangles display typical non-slip and slip regions. The lower-left insets correspond to selected area electron diffraction (SAED) patterns along the <011> β zone axis showing two ω ath variants reflections. The ω ath1 and ω ath2 are two crystallographic variants of the ω ath phase. (b,c) Dark-field images using the ω ath1 and ω ath2 reflections corresponding to the blue rectangle, which shows that the number of ω ath1 and ω ath2 precipitates is almost the same (~38) in non-slip region. These white speckles are the ω ath precipitates. White ω ath1 and ω ath2 precipitates are highlighted by green and blue dots, respectively. (d,e) Dark-field images corresponding to the red rectangle, which shows that in slip region the number of ω ath1 precipitates is near to zero and the number of ω ath2 (~74) is increased as double as the non-slip region. (f) STEM annular bright-field (ABF) lattice image shows dislocations pile-up in front of ω ath . They induce ω ath variant rotation and produce new dislocations on the rear of the rotated ω ath variant. Typical ω ath1 and ω ath2 crystal lattices are highlighted by six green and blue dots, respectively. The yellow arrow shows the slip direction. (g) Detailed characterization of the dislocations around ω ath precipitate in (f) by Geometric phase analysis (GPA) choosing (110) β and (112) β to calculate strain. Strain regions are highlighted by rectangles. The inset in the top left shows the fast Fourier transform (FFT) results of (f). The inset of two inverse FFT images with (110) β and (112) β reflections confirm that the highlighted strain regions by GPA are regions with dislocation. Full size image