Supplementary Figure 1: Geometry of the in situ tensile substrate. The dotted rectangle indicates the location where the TEM sample was placed.
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1 Supplementary Figures Supplementary Figure 1: Geometry of the in situ tensile substrate. The dotted rectangle indicates the location where the TEM sample was placed.
2 Supplementary Figure 2: The original HAADF-STEM image of Figure 2a without marks. The scale bar represents 0.5 nm.
3 Supplementary Figure 3: Structural variations between region I and II determined from another crack tip. a, Atomic-resolution HAADF-STEM image showing regions I and II with different crystal structures or orientations. The scale bar represents 1 nm. b, Distribution of the measured angle between two basic vectors (x and y) in the entire imaged area. c, A statistical profile of angle β for every 0.5 nm along the horizontal direction of the image; the average angle values with the uncertainty of measurement in every block are shown. The error bars represent the standard deviation.
4 Supplementary Figure 4: NDPs acquired from three different regions individually. a, region I, b, region II and c, region III in Fig. 2a. R1, R2 and R3 are defined as vectors between the transmission spot and the nearest, second nearest and third nearest diffraction spots.
5 Supplementary Figure 5: Typical NDPs mainly from region II at other crack tips.
6 Supplementary Figure 6: NDP for another orientation of the fcc phase. NDP obtained after tilting the sample ~19 away from the original viewing direction, including diffraction patterns of the [10-2] fcc, [114] bcc and [113] bcc zone axes.
7 Supplementary Figure 7: Atomic process of phase transitions. a-d, bcc1 fcc and e-h, fcc bcc2. b-d, enlarged images of the square area in a with one cyan-circle marked atom showing the transformation from the bcc1 to fcc lattice. f-h, enlarged images of the square area in e with another cyan-circle marked atom showing the transformation from the fcc to bcc2 lattice.
8 Supplementary Figure 8: The nucleation and growth of the fcc phase by successive local shears. The dashed circles in a-c indicate the locations of the local shears, while the arrows in all the subfigures indicate their moving direction along <110>. The atoms are colored according to their coordination number, white: 14 (bcc), blue: 13, yellow: 12 (fcc), maroon: 11, green: 10 and pink: 9.
9 Supplementary Figure 9: The physical process of the phase transitions bcc1 fcc bcc2. a-c, Viewed along [001] of the bcc1 phase (the viewing direction in the experiments). d-f, Viewed along [110] of the bcc1 phase, i.e., normal to the interface plane between bcc1 and bcc2. The V1 and V2 routes lead to the two bcc2 variants.
10 Supplementary Figure 10: Images showing different bcc1 and bcc2 relationships. a, HAADF-STEM image (scale bar represents 1 nm), b, HRTEM image for the [001] bcc1 //[1-11] bcc2 and (110) bcc1 //(110) bcc2 relationship (scale bar represents 3 nm), and c, HRTEM image for the [001] bcc1 //[1-11] bcc2 and (110) bcc1 +~10 //(110) bcc2 relationship (scale bar represents 3 nm).
11 Supplementary Figure 11: {112}<111> twins observed in MD simulations. The crack configuration is {001}<110>. Circles A and B: regions that start to re-orientate.
12 Supplementary Figure 12: {112}<111> twin observed in experiment. The crack configuration is {001}<110>. The scale bar represents 2 nm.
13 Supplementary Tables Supplementary Table 1: The ratios of R2/R1 and R3/R1 and angle φ and interplanar distance d R1 measured from the NDPs of Supplementary Fig. 4. Region R2/R1 R3/R1 φ( ) d R1 (nm) I II III
14 Supplementary Table 2: The angle φ measured in different NDPs from the fcc structure at different crack tips. φ ( ) Mean Standard deviation
15 Supplementary Notes Supplementary Note 1. HAADF-STEM image with bcc and fcc structures Similar to Fig. 2a, Supplementary Fig. 3a presents an HAADF-STEM image acquired from another crack tip with two different regions and a sharp interface. The orientation relationship between bcc1 and fcc is also (110) bcc1 //(111) fcc and [001] bcc1 //[10-1] fcc, which is the same as that in Fig. 2a. A similar analysis of the angle β between two basic vectors (x and y) is performed. In the profile result (Supplementary Fig. 3b), two peaks emerged at approximately 70 and 91 for regions I and II, respectively. A statistical analysis of the angle β for every 0.5 nm along the horizontal direction of the image was performed, and the average angle values with the uncertainty of measurement 1-3 for every block are shown in Supplementary Fig. 3c. Within each region, the angles are always near the characteristic angle (70.5 or 90 ) of <110>-orientated fcc or <100>-orientated bcc structures, except for a small fluctuation originating from the uncertainty of the measurement. Across the two regions, there is an abrupt angle change in a narrow area (~1 nm), which is indeed a boundary between the two structures. The results strongly indicate that a bcc fcc structure transformation occurs at the crack tip. The dimension of the fcc structure can reach as large as ~4 8 nm 2 here. Supplementary Note 2. Distinguishing the fcc structure from the bcc phase by electron nanodiffraction Supplementary Fig. 4 presents three electron nanodiffraction patterns (NDPs) acquired from every individual region I, II and III in Fig. 2a. For each NDP, R1, R2 and R3 are defined as vectors between the transmission spot and the nearest, second nearest and third nearest diffraction spots, respectively. The ratios of R2/R1 and R3/R1, the angle φ between R1 and R2 (here the angle φ is measured in reciprocal space, which corresponds to the angle β in real space in the HAADF-STEM images) and the interplanar spacing (d R1 ) of the crystallographic planes corresponding to R1 are measured from the NDPs in Supplementary Fig. 4 and listed in Supplementary Table 1. Comparing the measured results to the four parameters (R2/R1, R3/R1, φ and d R1 ) of a bcc Mo crystal (a = nm), the NDPs of regions I and III (Supplementary Fig. 4a and 4c) are undoubtedly determined to be the <001> and <111> zone axes of the bcc structure, respectively, while the NDP of region II (Supplementary Fig. 4b) does not fit any zone axis of the bcc structure. Nevertheless, upon comparison with the characteristic parameters (1.0, 1.15, 70.5 ) of the <110> zone axis of the reported fcc structure 4, the experimental data (1.0, 1.13, 70.3 ) matched well, and the lattice parameter of the fcc structure here was determined to be a = nm using d R1 = nm. This finding means that region II is most likely an fcc structure (or a structure with an fcc-like diffraction pattern along
16 this observed direction) rather than a bcc structure. NDPs with similar configurations as that in Supplementary Fig. 4b were detected at more than 10 crack tips in this work, and the angles in these NDPs were measured to be ~70.8 within an error of ±1.2 (SD, Supplementary Table 2). Typical NDPs from region II at other crack tips are shown in Supplementary Fig. 5. This result indicates that an angle of approximately 70.5 is a characteristic angle of the new structure, which is much different than the idea of continuous elastic distortion with a series of continuously varying angles between 60 and 90. Accordingly, the deformation behavior is related to structural transitions, and an fcc (or fcc-like) structure is identified. Supplementary Note 3. NDP in another orientation of the fcc phase After tilting the sample ~19 away from the original viewing direction, another NDP is obtained (Supplementary Fig. 6). The NDP in Supplementary Fig. 6 includes several sets of diffraction patterns. Two sets of patterns can be indexed as the <113> and <114> zone axes of the bcc crystal, and another set does not belong to a bcc crystal. The values of R2/R1, R3/R1 and the angle between R1 and R2 are approximately 2.24, 2.43, and 90, respectively. Here, R1, R2 and R3 are defined as vectors between the transmission spot and the nearest, second nearest and third nearest diffraction spots, respectively. This set of diffraction spots does not match with the diffraction patterns of any zone axis in the bcc or distorted bcc structure; however, this set belongs to the <102> zone axis of the fcc phase. The angle between the [10-1] fcc and [10-2] fcc axes is 18.4, which agrees well with the tilting angle of ~19 from the original [10-1] fcc direction in our experiment. The angle between [001] bcc and [114] bcc is 19.5 ; thus, the [114] bcc diffraction pattern will appear. However, in Supplementary Fig. 6, a [113] bcc diffraction pattern also appeared; the reason may be that the angle between [114] bcc and [113] bcc is as small as 5.8. When the electron beam is nearly parallel to [114] bcc zone axis, the reciprocal rods of some planes along the [113] bcc zone axis can intersect with the Ewald sphere and form diffraction spots. In fact, only two rows (indicated by the green arrows) of diffraction spots within the [113] bcc zone axis appear in Supplementary Fig. 6. A missing row of diffraction spots along the blue arrow in the scope of Supplementary Fig. 6 indicates the [113] bcc did not align well with the direction of the incident electron beam. Moreover, the effect of double diffraction in the complex diffraction pattern has been verified. The as-indexed fcc diffraction pattern was guaranteed as not being generated from any double diffractions of the bcc crystal. Supplementary Note 4. The mechanisms of the bcc1 fcc bcc2 phase transitions First, the atomic processes during the phase transitions bcc1 fcc and fcc bcc2 are revealed by MD simulation, as illustrated in Supplementary Fig. 7. All the figures (Supplementary Fig. 7) share the same lattice orientation as indicated in Supplementary Fig. 7a. The regions bounded by dashed lines in
17 Supplementary Figs. 7a and 7e are magnified in Supplementary Figs. 7(b-d) and 7(f-h), respectively. Supplementary Figs. 7(b-d) show one cyan-circle-marked atom in the original bcc1 lattice (white) transformed into an fcc-coordinate atom (yellow) by successive atomic shear along <110> bcc1 and small shuffles. The atomic image of the fcc region viewed along the <110> fcc direction is consistent with the viewing direction in the experiments (Figs. 2a and 4a). Supplementary Figs. 7(f-h) show the transformation from fcc to bcc2 via atomic shear on {111} planes of the fcc lattice with another cyan-circle-marked atom. The arrows in Supplementary Fig. 7d indicate the relative orientation of the bcc1 and fcc grains, while those in Supplementary Fig. 7h indicate the relative orientation of fcc and bcc2. The entire process is consistent with the N-W and K-S mechanisms. Furthermore, a possible mechanism of nucleation and growth of the fcc phase is revealed by the initial instantaneous configurations of the MD simulation results, as illustrated in Supplementary Figs. 8(a-f). The phase transformation is initiated by localized shears near the crack tip and proceeds by further propagation of these shears. As indicated by the dashed circles in Supplementary Fig. 8a, two shears occur at P1 and P2 propagating along [1-10] toward the lower right corner. P1 generates the first fcc layer, while P2 has just formed near the crack tip and is generating the second fcc layer. In Supplementary Fig. 8b, P1 and P2 further propagate, thickening the fcc nucleus, while P3 forms. In Supplementary Fig. 8c, both P1 and P2 stop as steps at the bcc/fcc boundary when they merged with another fcc region, and a two-layer fcc nucleus formed, while P3 further propagates and thickens the fcc nucleus. The repetition of this formation and propagation gradually extends the fcc phase (Supplementary Figs. 8(d-f)). Based on the N-W and K-S orientation relationships between bcc1-fcc and fcc-bcc2 structures, the mechanisms of these phase transformations are deduced and schematically illustrated in Supplementary Fig. 9. Here, (a-c) and (d-f) show the structural changes viewed along the [001] bcc1 (corresponding to the observation direction in the experiments) and [110] bcc1 (normal to the interface plane between bcc1 and bcc2 in Fig. 1) directions, respectively. The first transition, bcc1 fcc, obeys the N-W deformation process and consists of two steps. (1) The atoms in the (110) bcc1 planes shear in the [1-10] bcc1 direction, which reduces the angle θ from 90 to 70.5, as observed in Supplementary Figs. 9a to 9b. (2) The angle ω changes from 70.5 to 60 and is accompanied by small shuffles of atoms to form an fcc structure (Supplementary Figs. 9(d-e)). The second transition, fcc bcc2, follows the K-S process (Supplementary Figs. 9(b-c) and 9(e-f)) according to the V1 route in the Supplementary Fig. 9c: (i) The atoms in the (111) fcc planes shear in the [-211] fcc direction. The shear angle is (ii) A smaller shear occurs along the [-110] fcc direction in the (111) fcc planes, and simultaneously, the angle ω expands to (iii) Some atoms shuffle to form a bcc2 structure. According to the crystallographic symmetry of the fcc structure, two equivalent {111} planes ((111), (1-11)) belong to the same [10-1] zone, such that step (i-iii) may also proceed in the (1-11) plane (the
18 V2 route described in Supplementary Fig. 9c). The two bcc2 phase formed from routes V1 and V2 are variants. The two bcc2 variants are observed in the experiments shown in the HAADF-STEM images Fig. 2a and Supplementary Fig. 10a and in the HRTEM images Supplementary Figs. 10b and 10c.
19 Supplementary References 1. Du, K., Ernst, F., Pelsozy, M., Barthel, J. & Tillmann, K. Expansion of interatomic distances in platinum catalyst nanoparticles. Acta Mater. 58, (2010). 2. Seitz, H., Ahlborn, K., Seibt, M. & Schröter, W. Sensitivity limits of strain mapping procedures using high-resolution electron microscopy. J. Microsc. 190, (1998). 3. Du, K. & Phillipp, F. On the accuracy of lattice-distortion analysis directly from high-resolution transmission electron micrographs. J. Microsc. 221, (2006). 4. Häglund, J., Guillermet, A. F., Grimvall, G. & Körling, M. Theory of bonding in transition-metal carbides and nitrides. Phys. Rev. B 48, (1993).
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