Fig. 1. Deformation twinning in NPs with a Mn23Th6-type FCC structure (Fm3¯m, a = 1.24 nm). (a–c) BF-STEM images of the twinned monocrystalline FCC NPs in the cold-rolled and annealed Zr-0.8Sn-0.25Nb-0.35Fe (wt.%) alloy. The equivalent diameters of the NPs are ∼36, 242, and 182 nm, respectively. The twin boundaries (TB) are marked by yellow arrows. In (a), the moiré fringes observed on the NP, which would occur when the matrix and the NP were superimposed at a suitable mutual orientation [82], [83], [84], show a mirror symmetry referenced to the straight line in the NP, suggesting that twin formed in the NP. (d) A 3D atomic configuration of the Zr-octahedron-based network in a Mn23Th6-type FCC structure (Fm3¯m, a = 1.24 nm). (e, f) Atomic patterns of the FCC structure of the NP in (b) with superimposed atomic configurations of the Zr-octahedron-based network in (d) when viewed along the [1$\bar{1}$0] and [1$\bar{1}$1] directions, respectively. These atomic patterns were captured from Fig. S4.

Fig. 2. HRTEM, FFT, IFFT, and GPA analyses of the structure in the Mn23Th6-type FCC NP. (a) HRTEM image of the Mn23Th6-type FCC structure along the [1$\bar{1}$0] direction. (b) FFT pattern corresponding to (a). (c) IFFT image obtained after Fourier masking the whole FFT pattern in (b). (d) IFFT image obtained after Fourier masking the 1st order (111) FFT spots in (b). (e, f) The in-plane εyy map along the [111] direction and the defined εxy map obtained by the GPA analysis of (d) referenced to an orthogonal lattice network composed of (111) and ($\bar{1}$$\bar{1}$2) planes as the yellow arrows in (d) indicate, respectively.

Fig. 3. FFT, IFFT, and GPA analyses of the matrix/TB/twin structure in the Mn23Th6-type FCC NP in Fig. 1(b). (a) FFT pattern of the matrix /TB/twin structure along the [1$\bar{1}$0] direction in Fig. S5(b). (b) IFFT image obtained after Fourier masking the whole FFT pattern in (a). (c) IFFT image obtained after Fourier masking the 1st order (111) FFT spots as yellow circles marked in (a). (d–f) The in-plane εyy map along the [111] direction and the defined εxy map obtained by the GPA analysis of (c) referenced to an orthogonal lattice network composed of (111) and ($\bar{1}$$\bar{1}$2) planes as the yellow arrows indicated in Fig. 2(d).

Fig. 4. Atomic displacements and shear distributions in the transition state of deformation twinning in the Mn23Th6-type FCC NP. (a) IFFT image created by tailoring Fig. 2(c), only showing the atomic-scale structures at and near the TB. (b, c) Zoomed-in IFFT images of the left and right sides of (a), respectively, showing the transition states of deformation twinning. (d) The atomic configuration projections of the transition state of deformation twinning extracted from (c). (e) The atomic configuration projections of the unstrained matrix structure and the almost fully twinned structure extracted from (c), showing the shear deformation during the full deformation twinning process. (f) Phase brightness analysis of atomic columns on Line B1B10’ and C1C10’ in (c), which are colored by blue and purple, respectively; black vertical lines show the positions where the Zr-octahedra is supposed to be either in the unstrained matrix structure or in the fully twinned structure as a reference for comparison. (g, h) Longitudinal strains and engineering strains along the [$\bar{1}$$\bar{1}$2] direction calculated based on the phase brightness analysis in (f), respectively. The blue and purple curves represent the strains in Plane B’ and C’ as a function of atomic distance, respectively; the black lines correspond to the zero-strain in the unstrained matrix structure or the fully twinned structure as a reference for comparison.

Fig. 5. Mechanisms underlying deformation twinning in FCC structures. (a) Shear strain energy stored in the transition state of deformation twinning as shown in Fig. 3(d), namely, the energy barrier needed to be overcome for nucleation of deformation twinning. (b) Illustration of domino effect. (c) Schematic illustration of the deformation twinning route based on our results here. The deformation twinning propagation is analogous to domino effect.

Fig. 6. Loading criterion for deformation twinning of a monocrystalline FCC NP. (a, b) BF-TEM image of the twinned NP in Fig. 1(c) and its corresponding schematic illustration. (c) 3D atomic structure of the [$\bar{1}$$\bar{1}$2](111) twin system. (d) Schematic relation of loading stress, σ, with the [$\bar{1}$$\bar{1}$2](111) twin system. The loading stress is constrained in the planed determined by the twinning plane normal and the twinning direction and defined by β and θ, angles between the loading direction and a-axis and c-axis, respectively. (e) Schmid factors of the [$\bar{1}$$\bar{1}$2](111) twinning under σ as a function of θ. (f) Schematic illustration of the optimal scenario for driving deformation twinning of a monocrystalline FCC NP under uniaxial compression.