Main

Large capability of superelastic deformation in structural materials is desirable for practical mechanical devices and flexible electronics1,2,3,4,5. Unlike the non-directional and delocalized metallic bonds, which can easily drive the displacive movement of atoms for structural transition in metals and thus realize superelasticity with large deformation therein (Fig. 1a), the directional and saturated nature of chemical bonds in inorganic non-metallic materials typically hinders such structural transitions and is not expected to facilitate superelasticity6,7,8,9,10. In ceramic crystals, the interaction between neighbouring atoms dominated by repulsion at short distances and attraction at long distances (similar to the Lennard-Jones potential11,12 shown in Fig. 1b) plays an important role in their elastic mechanical properties. Owing to the strong asymmetry of the Lennard-Jones potential curve far from the equilibrium position (the potential quickly diverges with atoms getting closer while slowly saturating to zero potential energy with atoms getting farther apart), the atom interactions shown in the Lennard-Jones potential behave in different ways under tension and compression limits13, respectively, thus leading to variations between tensile and compressed superelasticity14. Although superelasticity under compressive stress has been observed in two specific ceramic crystals (ZrO2 and BaTiO3)15,16,17, tensile superelasticity has not been observed in ceramic crystals.

Fig. 1: Observation of emergent superelasticity in ceramic crystal GeSe.
figure 1

a, Schematic of the stress–strain relationship for tensile and compressive superelastic deformations during the loading and unloading process. b, Schematic illustration of the interatomic potential as a function of atom distance. Here R denotes the distance between two interacting atoms, while σ represents the distance at which the potential energy equals zero. c, Crystal structure of GeSe (space group Pnma) viewed along the [100] direction. The purple and green balls represent Ge and Se atoms, respectively. d, Schematic diagram for the in situ uniaxial tensile equipment via the DT method. e, TEM image of GeSe nanobridges and diamond tensile gripper for the tensile test. f–h, In situ TEM images of the GeSe sample (sample A) before loading (f), at the beginning of superelasticity emergence (g) and at the maximum load (h). i, Stress–strain curve of a typical GeSe sample measured via the DT method. The critical strain for the emergence of superelasticity is roughly determined as the intersection of the tangent lines of the data in the linear elastic region and superelastic plateau region.

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GeSe is a layered ceramic crystal and possesses unique structural and bonding characteristics: (1) its puckered orthorhombic lattice (Fig. 1c and Extended Data Fig. 1) enables notable elastic deformation under low stress18,19, (2) its in-plane anisotropy creates distinct mechanical properties along the zigzag and armchair directions20, and (3) its metavalent bonding, which lies between metallic and covalent bonds, provides a balance of mechanical flexibility and electronic functionality21,22,23. These features make GeSe an ideal candidate for exploring tensile superelasticity in ceramics.

In this work, we demonstrate directional tensile superelasticity in GeSe. With in situ mechanical high-resolution transmission electron microscopy (HRTEM), we unveil the stress–strain response; the linear elastic behaviour evolves into a superelastic plateau at a critical strain, which is accompanied by the simultaneous generation of stripy-shaped twin domains along the <110> orientation. These stripy-shaped twin domains grow rapidly in width with a further increase in strain. Notably, the twinning-driven superelasticity is anisotropic and only emerges at strain angles close to the zigzag direction. First-principles calculations reveal that the shuffle twinning process, which is based on the bond-configuration change from Z-shape to anti-Z-shape, leads to a release of elastic potential energy in GeSe and yields superelastic behaviour. This anisotropic mechanism for achieving superelasticity is distinct from the common martensitic transformation mechanism for superelasticity in metals. Our findings not only establish an alternative mechanism for achieving tensile superelasticity in ceramic crystals but also offer opportunities for designing advanced semiconductor materials with tailored mechanical properties, for example, for integration into flexible electronics or mechanical systems.

Superelasticity in GeSe ceramic crystal

We prepared GeSe samples and conducted in situ TEM tensile measurements using push-to-pull (PTP)24 and direct-tensile (DT)25 methods (Methods, Fig. 1d,e, Extended Data Fig. 2 and Supplementary Fig. 1). Figure 1i shows the stress–strain curve for a typical DT sample (150 nm thick), where the stress–strain responses and TEM images (Fig. 1f–h) were collected simultaneously with stress applied along the zigzag direction, as further illustrated by in situ dark-field TEM images in Supplementary Fig. 2. In Fig. 1i, the GeSe sample initially shows linear elastic behaviour, transitioning to near-plateau stress behaviour when the strain exceeds 2.5% (Supplementary Fig. 3). Simultaneously, certain stripy domains emerge, as shown by TEM images, forming only at specific angles (47° ± 2° or 133° ± 2°) relative to the zigzag direction (Extended Data Fig. 3 and Supplementary Table 1), which implies that the domain boundaries prefer to form along certain high-symmetric crystallographic directions. Consistent with the superelastic loop, both the emergence and the disappearance of stripy domains can be confirmed with strain loading and unloading (Fig. 1f–h, Supplementary Fig. 2 and Supplementary Videos 1–3). The occurrence of superelasticity in GeSe is influenced by sample dimensions and strain rate (Supplementary Figs. 4–6). However, the reversible stripy twin domains and consistent critical strain (~2.5%) are highly reproducible, confirmed in over 44 GeSe samples (Supplementary Figs. 3, 7 and 8, and Supplementary Table 1). Since such a loop-shaped stress–strain curve is always regarded as the typical behaviour for superelasticity, which has been widely observed in those superelastic metallic alloys driven by martensitic transformation3,10, these results might indicate that the superelastic behaviour in GeSe ceramic crystal is microscopically associated with the reversible formation of stripy domains.

Reversible shuffle twinning mechanism

To investigate the microscopic formation of superelasticity in GeSe ceramic crystal, we performed in situ HRTEM imaging on PTP samples to examine the evolution of atomic domain structures under strain (Fig. 2a–c, Extended Data Fig. 4, Supplementary Fig. 1b and Supplementary Videos 4 and 5). Figure 2a–c, along with Supplementary Video 4, shows a sample viewed along the c direction during loading in the zigzag direction of GeSe. By contrast, Extended Data Fig. 4 and Supplementary Video 5 depict another sample viewed along the armchair direction during loading (Supplementary Fig. 1b). Figure 2a shows four stages during the evolution of stripy domain with strain loading: (1) the stripy domain emerges at 69 s, coinciding with the transition of the stress–strain curve to superelastic behaviour; (2) the stripy domain grows to ~15 nm in width by 105 s, corresponding to the nonlinear superelastic regime; (3) during strain unloading (105–123 s), the domain width remains unchanged owing to the recovery of the linear elastic strain; (4) after full strain release, the domain narrows and disappears, resulting in nonlinear superelastic recovery (Supplementary Fig. 9). This reversible formation and disappearance of stripy domains underlie the superelastic loop behaviour in GeSe ceramic crystal.

Fig. 2: Evolution of the stripy twin domain in GeSe under tensile loading and unloading strains.
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a, High-resolution TEM snapshots taken along the <001> zone axis of the GeSe sample (sample B) under the loading and unloading strains. b,c, The FFT pattern (c) of the HRTEM image (b) corresponding to the region containing a twin domain. The scale bar in the FFT pattern is 5 nm−1. d–f, HAADF-STEM image (d), corresponding structural model (e) and simulated HAADF-STEM image (f) of a twin boundary. Here HRTEM and HAADF-STEM images of sample B, obtained via the PTP method, reveal twinning behaviour in the first cycle and atomic-resolution details of twinning structure formed in the subsequent cycle. g, Top: the energy profile of the twinning transformation pathway at different strain values. Arrows indicate the energy saddle points. The inset schematic illustrates the bond breakage and formation during twinning/detwinning in GeSe under uniaxial strain along the zigzag direction. Here the energy of the initial state is set as zero energy. Bottom: the corresponding distance changes of Ge1–Se1 and Ge1–Se2 atoms during the twinning process. d1 and d2 represent the bond lengths of Ge1–Se1 and Ge1–Se2, respectively. The bond length for GeSe without strain is calculated to be 2.60 Å. h, The final energy, twinning barrier and detwinning barrier as a function of strain.

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To confirm the crystal structure of newly formed stripy domains, we performed fast Fourier transform (FFT) analysis for the matrix and stripy domain region in HRTEM images. As shown in Fig. 2b,c, the stripy domain shares the same crystal structure and lattice symmetry as the matrix, with their zigzag directions rotated by 82.5° relative to each other. The stripy twin domain is connected to the matrix region through highly coherent interfaces, with twin boundaries oriented along the <110> direction of the matrix, as revealed by atomic-scale high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images (Fig. 2d–f, Extended Data Fig. 5 and Supplementary Fig. 10). This evidence confirms that the superelasticity in GeSe ceramic crystal originates from reversible twinning processes rather than phase transformations. Interestingly, twins tend to nucleate at locations with high stress concentrations, such as surfaces and local defects (Supplementary Fig. 11). This twinning process can serve as an alternative mechanism to generate the superelasticity in ceramic crystals, distinct from the martensitic-transformation-driven superelasticity in shape memory alloys3,10.

We performed ab initio total energy calculations to understand the energetically favourable twinning crystal structures under varying tensile strains (Fig. 2g). Two key points are highlighted in Fig. 2g. First, the twin structure becomes more stable at larger strains, as shown by the notable reduction of final state energy with increasing strain (Fig. 2h). The relative energy of the final state to the initial state decreases to a negative value as the strain reaches 7%, indicating that such a strain drives twin structure formation. Second, twinning under strain can occur spontaneously even at room temperature as the energy barrier for twinning decreases to below 5 meV per atom with increasing strain. This ultralow barrier suggests that even mild exothermic reactions under large strain can drive twin domain formation, enabling an easy route to superelasticity.

As shown in the cartoon atomic configuration in the inset of Fig. 2g and Extended Data Fig. 6a,b, the spontaneous twinning process microscopically arises from changing between the Z-shaped and anti-Z-shaped atomic configurations along the [110] direction. As the in-plane Ge1–Se1 bond stretches under tensile strain and the surrounding non-bonded Ge and Se atoms (for example, Ge1–Se2) move closer, the strain eventually breaks the Ge1–Se1 bond and forms a new Ge1–Se2 bond (Fig. 2g and Supplementary Fig. 12). This twining process, induced by Z-shaped to anti-Z-shaped bond switching, involves the collective rotation of Ge–Se atom pairs arranged in the [110] direction and can be regarded as the shuffle twinning process. The bond-switching-mediated twinning processes in GeSe occur at a much lower energy cost compared with slip-induced stacking fault mechanism (Supplementary Fig. 13). In contrast to the abrupt atom rearrangement in structural transitions, the uniform atomic shuffling in typical twinning processes can always introduce fewer lattice defects and lower residual stress in materials, considerably reducing the risk of material failure and cracking26,27.

To understand the twin formation dynamics in GeSe ceramic crystal, we performed ab initio molecular dynamics (AIMD) simulations under uniaxial strain (Methods, Fig. 3a–c, Supplementary Figs. 14–16 and Supplementary Video 6). Figure 3b,c shows the stress–strain and the energy–strain curves from the AIMD simulations. The simulations revealed that once a Ge–Se atom pair rotates to drive Z-shaped to anti-Z-shaped bond switching, it promotes the rotation of adjacent pairs, rapidly forming and growing twin domains within an ultrafast picosecond timeframe (Fig. 3a). Correspondingly, the energy–strain curve of twinning GeSe deviates dramatically from the expected elastic behaviour of untwined GeSe, with the calculated energy of the twin domain structure being much lower (Fig. 3b). This indicates that twin domain formation reduces the elastic energy, making twinning and nonlinear superelasticity feasible under strain. In addition, we confirmed that the formation of new twin domains causes a stress drop in the stress–strain curve, demonstrating that the required stress for a target strain is substantially reduced after twinning. This demonstrates that twin domain formation is the dominant mechanism for the nonlinear deformation in GeSe ceramic crystal. For example, Fig. 3b,c and Extended Data Fig. 6c show that stress and energy drops occur at 6% and 9% strain owing to the formation of new twin domains, which release elastic energy and drive nonlinear superelastic behaviour during loading. In the calculation, twins may form at higher strains, possibly owing to model size limitations that overestimate twin proportions. Our AIMD simulations, consistent with experimental observations, confirmed that the reversible shuffle twinning process drives superelasticity. Interestingly, the shuffle twinning mechanism and resulting twin domains were also experimentally observed in sulfide-based GeS ceramic crystals with the same puckered structure (Extended Data Fig. 7), suggesting that this mechanism could be a universal strategy for inducing superelasticity in other ceramic crystals.

Fig. 3: Local lattice strain analysis of GeSe under tensile strain loading–unloading.
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a, Statistical averages of the structure in different time intervals for the molecular dynamics of GeSe under 6% strain along the [100] direction. AB represents the stacking sequence of the original lattice. The model images cross 32 primitive cells of GeSe. b, Calculated energy of GeSe as a function of strain along the zigzag direction. c, Simulated stress–strain curve of GeSe as a function of strain along the zigzag direction. d–f, Evolution of the stripy domain width (f), in-plane lattice parameters (d) and derived local in-plane lattice strains in the matrix and stripy domain (e) during the loading–unloading tensile strains of sample C obtained using the PTP method. The local lattice strain is derived by ε = ΔL/L, where L is the lattice parameter along the zigzag or armchair direction and ΔL is the corresponding change of lattice parameter under stress. In the first loading–unloading cycle, loading and unloading begin at 86 s and 200 s, respectively, while in the second cycle, loading and unloading begin at 285 s and 356 s, respectively. L1 and S1 indicate the linear elastic stage and the nonlinear superplastic stage during loading, respectively, while L2 and S2 represent the linear elastic stage and the nonlinear superplastic stage during unloading. The two loading–unloading cycles are extracted from Supplementary Video 7. Here the HRTEM dataset from the first and second cycles of sample C, obtained using the PTP method, highlights the evolution of lattice parameters across multiple cycles, complementing the data in Fig. 2.

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Lattice evolution during superelastic deformation

To better understand the superelastic behaviour in GeSe crystal at the atomic scale, we extracted in-plane lattice parameters from HRTEM images and analysed their evolution during the strain loading–unloading process (Fig. 3d–f, Extended Data Fig. 8, Supplementary Fig. 17, Supplementary Table 2 and Supplementary Video 7). Consistent with the discussion above, the in-plane lattice strain evolution in each cycle can be divided into four regions, including two linear regions during initial loading (L1) and unloading (L2) and two superelastic regions during loading (S1) and unloading (S2). In region S1, after the critical strain for twin domain formation, the lattice parameter along the armchair direction of the twin domain is stretched (owing to a twinning angle of ~82.5°), and the lattice strain dramatically increases to 5.8% with rapid twin domain growth, while the matrix lattice strain along the zigzag direction decreases from 2% to 1%. Interestingly, the formation and rapid growth of twin domains enhance the GeSe deformation, resulting in observed superelasticity along the matrix zigzag direction, as the lattice parameter along the armchair direction (b = 4.38 Å) is much larger than that along the zigzag direction (a = 3.81 Å). On the basis of the sample’s modulus and measured lattice strain, we estimated the stress–strain curves, which exhibit a clear hysteresis feature (Supplementary Fig. 18) and align well with those obtained via DT testing. Notably, the lattice parameter evolution and lattice strain behaviour in both the first and second cycles are nearly identical, demonstrating excellent recyclability of GeSe’s superelastic behaviour.

Generally, the maximum strain εmax can be estimated by the following formula:

$${\varepsilon }_{\max }=\frac{xb\left(1+\varepsilon _{\max }^{{\rm{ac}}}\right)+(1-x)a\left(1+\varepsilon _{\max }^{{\rm{zz}}}\right)}{a}-1$$

where \({\varepsilon }_{\max }^{{\rm{ac}}}\) and \({\varepsilon }_{\max }^{{\rm{zz}}}\) are the maximum local strains that can be reached before the fracture along the armchair and zigzag directions (Supplementary Fig. 19), and x is the proportion of the matrix that has transformed into twin domains. a and b refer to the lattice parameters of GeSe, with values of 3.81 Å and 4.38 Å, respectively. According to the local lattice strain analysis in Fig. 3e, the observed largest values of \({\varepsilon }_{\max }^{{\rm{ac}}}\) and \({\varepsilon }_{\max }^{{\rm{zz}}}\) can be estimated to be ~5.8% and ~2.9%, respectively. Assuming that half of the matrix transforms into twin domains (x = 0.5), the maximum strain is theoretically ~12.3%. Experimentally, with stripy domain formation, a maximum strain of ~12.8% is achieved before GeSe sample fracture (Extended Data Fig. 9), aligning well with theoretical predictions. Twinning elements26 obtained from HRTEM show a twinning shear of ~0.30, also consistent with theoretical estimates (Supplementary Fig. 20). Although twinning shear may cause localized nonuniform deformation, this deformation recovers after unloading (Supplementary Fig. 21) if no cracking occurs within the twin domain (Supplementary Fig. 22 and Supplementary Video 8). Compared with other layered materials, GeSe’s small Young’s modulus and twinning-induced superelasticity enable a large strain limit (Supplementary Fig. 23 and Supplementary Table 3), offering great potential for advanced mechanical applications28,29,30. In addition, compared with other well-known superelastic materials, GeSe offers unique features such as a large strain limit, excellent cyclability (Supplementary Figs. 24 and 25, Supplementary Table 4 and Supplementary Video 9), an alternative superelastic mechanism and its distinctive two-dimensional semiconductor properties.

Directional superelasticity

To confirm the stress directions exhibiting the superelasticity in GeSe, we performed the tensile–strain measurements based on PTP samples with the bridge oriented at different angles (θ, the angle between the zigzag and loading directions). Unlike the superelastic behaviour observed under strain along the zigzag direction, GeSe samples subjected to strain along the armchair direction show only reversible linear elastic behaviour, without stripy domain formations, before fracturing at ~5% strain (Supplementary Fig. 26). This suggests that GeSe superelasticity is highly dependent on the loading direction. Figure 4a shows in situ TEM images of PTP samples with θ ranging from 0° to 180° (Extended Data Fig. 10). Observable stripy domains (indicative of superelasticity) appear only when θ is between 325° and 30° (or 145° and 210°). At all other angles, no stripy domains are observed, even when samples are stretched to fracture. Young’s modulus of GeSe along the armchair direction is ~27 GPa, much smaller than that along the zigzag direction (~40 GPa), suggesting that this anisotropic Young’s modulus may underlie the directional superelasticity in GeSe31.

Fig. 4: Directional superelasticity in GeSe ceramic crystal.
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a, Loading direction dependence of superelasticity in GeSe. TEM images showing typical fabricated GeSe samples for PTP testing, featuring different bridge orientations with respect to the zigzag direction. Insets: SAED patterns of the tested samples. The zigzag direction of each sample is indexed by a red arrow, and the stripy domains generated owing to tensile strain are highlighted by blue dashed lines. The black dashed lines indicate the fracture of the tested samples under a large strain. Middle inset: schematic diagram illustrating the range of tensile directions for the appearance of superelasticity in GeSe. The balls represent the experimentally measured values of θ, among which the orange balls highlight the superelastic case and the blue balls highlight the elastic case. b, The calculated Young’s modulus of GeSe along different directions. Angle of 0° indicates the strain along the zigzag ([100]) direction. c, Poisson’s ratio and convergence coefficient τ along different directions. τ indicates the ease of convergence between a and b with axial tensile strain. Inset: the orientation of GeSe crystal. d, Top view of charge density difference between a GeSe structure with one Ge–Se pair rotated by 90° and one without bond rotation. Ge and Se atoms are coloured in purple and green, respectively. The red and blue bubbles indicate the increase and decrease of the charge density, corresponding to the electron dissipation and collection, respectively.

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We calculated Young’s modulus of the matrix and twin domains along specific tensile directions. As shown in Fig. 4b, the angle-dependent Young’s modulus shows strong anisotropy along zigzag and armchair directions, consistent with the experimental results. Twinning generally occurs during the loading to release elastic energy, but only when the matrix’s Young’s modulus greatly exceeds that of the twin domain, as observed for loading directions near the zigzag direction (Supplementary Fig. 28). To achieve the transition state in Fig. 2g and interchange the zigzag and armchair directions of GeSe, the loading direction must enable convergence of lattice lengths a and b. The calculated Poisson’s ratio decreases from +1.13 along the zigzag direction (θ = 0) to negative values in the interval 40° < θ < 50°, and then increases to +0.39 along the armchair direction (Fig. 4c and Supplementary Fig. 27). A convergence coefficient τ, related to Poisson’s ratio, indicates the ease of convergence between a and b (Supplementary equation (7)). τ decreases as θ increases, and convergence occurs only when τ is positive—the higher the value, the easier the convergence. Thus, a approaches b most rapidly at θ = 0, but slows and is inhibited as θ increases (Fig. 4c, details in Supplementary Information). These calculations align with experimental observations, where twinning and superelasticity occur under tensile loading at θ <~40°.

To understand the relationship between directional Ge–Se bonds and the twin domain (observed in Figs. 1f–h and 4a), we calculated the charge density difference between a GeSe structure with one Ge–Se pair rotated by 90° and one without rotation (Fig. 4d). Rotating a single Ge–Se pair causes a considerable perturbation in the charge density, more pronounced along the [110] direction than [100] and [010] directions. This large charge perturbation destabilizes the local electron structure, prompting bond reconstruction. When an adjacent Ge–Se pair along the [110] direction rotates owing to this perturbation, the effect propagates further along the same direction. This agrees with MD simulation (Supplementary Video 6), which shows that shuffle twinning rapidly originates from a single Ge–Se pair rotation. It also explains the fast nucleation and growth of twins along the [110] direction in experiments. Therefore, directional bonding plays an important role in the formation of directional twin domains in GeSe, providing a platform to modulate the mechanical properties of ceramic crystals (Supplementary Fig. 29).

Conclusion

We observed anisotropic tensile superelasticity in ceramic crystal GeSe. The underlying reversible shuffle twinning mechanism, which is distinct from the structural transition-driven superelasticity in metallic alloys, may be also operational in other ceramic semiconductors with similar crystal structures32,33, including but not limited to SnSe, SnS, GeS and their doped counterparts (Supplementary Figs. 30 and 31 and Supplementary Tables 5 and 6). Mechanical-stimuli-driven ferroelasticity has been demonstrated in chalcogenides34, and intrinsic ferroelectricity is known in structurally analogous materials35,36. The discovery of tensile superelasticity in GeSe raises hope for coexisting ferroelastic, ferroelectric and superelastic behaviour in this material class—a multiferroic coupling mechanism analogous to domain-engineered functionalities in BiFeO3, where twin boundaries host emergent properties such as interfacial conductivity and photovoltaic effects37,38. While experimental evidence of this interplay in GeSe is still lacking, the strain-dependent twinning–detwinning process, combined with chalcogenides’ spin helicity39, nonlinear optics40 and bulk photovoltaic effects41,42, provides a promising starting point for the development of strain-modulated optoelectronics. For example, mechanically responsive devices, such as photodetectors or sensors, could utilize strain-induced electronic state modifications, similar to domain-wall-enabled functionalities in BiFeO3. With further advances in heterostructure engineering and localized property characterization, these concepts could be translated into practical applications. Texture engineering and doping strategies together with the extension beyond single-crystal GeSe to polycrystalline materials or other ceramics with different bonding characteristics could help broaden the scope for potential applications of anisotropic tensile superelasticity.

Methods

Fabrication of microscale GeSe samples for TEM tensile strain testing

GeSe single crystals were synthesized via the chemical vapour transport method43. GeSe flakes for in situ TEM experiments under tensile strain were fabricated by using a focused ion beam (Helios G5, Thermo Fisher Scientific) as follows. First, a thin lamella was milled from as-grown crystals with the polished surface, and then it was cut and transferred onto a TEM half-grid fixed by Pt welding. Second, the lamella was laterally narrowed to a width of 3 μm and then further shaped into a nanobridge specimen with dimensions of 100–300 nm in width and 1–3 μm in length. The diamond gripper was specifically designed with a diamond indenter tip to grip the nanobridge specimen for tensile testing. The presence and orientation of the twins in the lamella were ascertained via TEM observation and corresponding electron diffraction analysis. A thin surface amorphous layer with a few nanometres thickness typically forms on the GeSe sample after focused ion beam milling, which has a minimal impact on the twinning-mediated superelasticity in GeSe owing to its minimal thickness and low mechanical properties (Supplementary Figs. 32–34).

In situ TEM and STEM characterization

In situ PTP tensile tests were performed with a positioning control of 0.1 nm in a custom-designed X-Nano TEM system44. The in situ DT tensile experiments were conducted with a displacement loading rate of 1.0 nm s−1 using a Hysitron PicoIndenter PI95 (Hysitron). The PTP method provides stability for applying strain to very thin samples, making it ideal for HRTEM measurements, while the DT method allows for direct stress–strain measurements. All in situ mechanical tests were performed in a JEM-ARM200F microscope (JEOL) at 200 kV. All STEM observations were performed in an aberration-corrected JEM-ARM300F2 (JEOL) at 300 kV with a 25 mrad probe convergence angle. HAADF images were captured by using 60–200 mrad inner-out collection angles. STEM imaging of the twin structures involved transferring the sample, mounted on the X-Nano stage, from the image-corrected JEM-ARM200F—where the twin domains were initially identified—to the probe-corrected JEM-ARM300F2. The sample was reloaded until the twin domains reappeared, and stress was maintained to stabilize them, enabling the capture of high-resolution images. The details of the in situ TEM and STEM characterizations can be found in Supplementary Information. Corresponding HAADF-STEM image simulation was conducted according to the experimental imaging parameters by using a developed software45.

Density functional theory calculations

The structure and mechanical properties of Pnma-GeSe were simulated by using the projector-augmented wave46 method as implemented in the VASP code47. Generalized gradient approximation with the functional of Perdew, Burke and Ernzerhof48 was adopted to treat the exchange-correlation energy. The energy barrier was calculated by the climbing-image nudged elastic band method49. The model used for calculating the transition state is a 2 × 2 × 1 supercell containing 32 atoms, as illustrated in Extended Data Fig. 6a. The dynamic evolution of GeSe under loading and unloading processes was simulated through alternative structure optimization and molecular dynamics. Strain along the zigzag direction is applied step-by-step on a periodic model containing 256 atoms in a cell, constructed using a transformation matrix of \(\left(\begin{array}{ccc}2 & 2 & 0\\ -8 & 8 & 0\\ 0 & 0 & 1\end{array}\right)\) applied to the primitive cell, as shown in Extended Data Fig. 6c. After relaxing the lattice and atom positions at each strain, AIMD at 300 K was carried out for at least 10 ps (time step of 1 fs, 10,000 steps) to check the dynamic stability. The canonical ensemble (NVT) with a Nosé–Hoover thermostat was used50. If the structure was unstable and transformed to another configuration within the first 10 ps, a simulation with an additional 10 ps was run until the structure stabilized. The structure, energy and stress of the final state are determined by averaging the atomic positions in the last 1 ps and re-relaxing the configuration. In the molecular dynamics simulation, an energy cut-off of 320 eV, a k-point of Γ and an energy convergence criterion of 10−6 eV were used. In relaxation, to obtain more accurate energy and stress data, an energy cut-off of 500 eV, a k-point resolution of 2π × 0.04 Å−1, an energy convergence criterion of 10−6 eV and a force criterion of 0.01 eV Å−1 were used. To determine the directional Young’s modulus and Poisson’s ratio, we calculated the elastic tensor of intrinsic GeSe by applying finite distortions to the lattice and deriving the elastic constants from the stress–strain relationship. This calculation was performed using the VASP code with the parameters IBRION = 6 and ISIF = 3. Subsequently, Young’s modulus and Poisson’s ratio as functions of the direction angle (θ) were obtained by applying a coordinate system transformation to the elastic tensor matrix.