Room-temperature oxygen vacancy migration induced reversible phase transformation during the anelastic deformation in CuO

From the mechanical perspectives, the influence of point defects is generally considered at high temperature, especially when the creep deformation dominates. Here, we show the stress-induced reversible oxygen vacancy migration in CuO nanowires at room temperature, causing the unanticipated anelastic deformation. The anelastic strain is associated with the nucleation of oxygen-deficient CuOx phase, which gradually transforms back to CuO after stress releasing, leading to the gradual recovery of the nanowire shape. Detailed analysis reveals an oxygen deficient metastable CuOx phase that has been overlooked in the literatures. Both theoretical and experimental investigations faithfully predict the oxygen vacancy diffusion pathways in CuO. Our finding facilitates a better understanding of the complicated mechanical behaviors in materials, which could also be relevant across multiple scientific disciplines, such as high-temperature superconductivity and solid-state chemistry in Cu-O compounds, etc.

T he structural stability of material subjected to intense mechanical duress is the corner stone for ensuring the robust performance in micro-electro-mechanical systems and devices, whereas there is a surging demand for the effective damping system to minimize mechanical vibration or noise 1,2 . Toward this end, the anelasticity, characterized by a delay in the shape recovery after retracting the external stress and thus extensively utilized to dissipate the mechanical energy, has been the focus of research for decades [3][4][5] .
In contrast to conventional anelastic behaviors, which generally involve the cooperative motion of atoms at grain or phase boundaries in polycrystalline or composite materials [6][7][8] , the unexpected remarkable anelasticity was reported in single crystalline (e.g., ZnO) nanowires (NWs) recently 9 . It was speculated that the point defect migration in an inhomogeneous stress field, called as Gorsky effect, might account for the observed damping process in single crystalline materials [10][11][12] . In nanosized materials, the generalized, nonlinear Gorsky effect associated with short diffusion distance and large stress gradient (under bending), could contribute to a much larger anelastic strain, even at room temperature 9 . Nevertheless, the experimental verification of this mechanism has suffered from the difficulty in directly resolving point defects 13 , especially when they are mobile under the external stress. More recently, it was theorized that the localized bond stretching and compression 14 rather than the vacancy migration can induce the anelasticity in single crystalline materials, making the underlying anelastic deformation mechanisms elusive and thereby stunting development for device design and modelling.
Our findings provide the direct atomistic view regarding the point defect migration in nanosized materials at room temperature 9 .

Results and discussion
The bending tests were performed with a Nanofactory EP1000 transmission electron microscopy-scanning tunneling microscopy (TEM-STM) holder inside the TEM [29][30][31] . After bending stress releasing, the single crystalline CuO NW undergoes an instantaneous elastic strain recovery followed by gradual recovering of anelastic strain (Fig. 1a, b, see also Supplementary Fig. 1 and Supplementary Movie 1). Figure 1c reveals that the large anelastic strains (up to 0.46%) in CuO NWs, comparable to those reported in ZnO NWs (as large as 0.64%), substantially recover in 2-3 min. Moreover, the anelasticity also exists when electron beam (e-beam) is turned off, indicating that it is an intrinsic property of single crystalline CuO NWs ( Supplementary Fig. 2). To clarify the controversial anelastic deformation mechanisms in single crystalline materials, further atomic-scale structural characterizations were performed. The high-resolution TEM (HRTEM) image in Fig. 1d (the inserted fast Fourier transformation (FFT) image) shows the formation of a different phase at the compressive end of the CuO NW at the moment when the bending stress is removed (enclosed area in Supplementary  Fig. 3). Consistently, the anelastic strain recovery (Fig. 1e) is associated with the gradual transformation of nucleated phase to monoclinic CuO structure (space group: C2/c) (see also Supplementary Fig. 4 and Movie 2). The electron energy-loss spectroscopy (EELS) and energy dispersive spectroscopy (EDS) spectra (red line in Fig. 1f   is between 1+ and 2+, i.e., x ranges from 0.5 to 1 32 . However, to our best, the CuO x phase (Fig. 1d) cannot be indexed based on any reported Cu-O compound structure reported hitherto.
First-principles calculations combined with cluster expansion construction method 28 were applied to reveal the atomic structure of CuO x . Alloy Theoretic Automated Toolkit (ATAT) is a collection of alloy theory tools 33 , which could automate alloy phase diagram calculations by atom substitutions (Fig. 2a). Among all the calculated phases, a typical CuO 0.67 (i.e., Cu 3 O 2 ) phase with unreported monoclinic structure (space group: C2/m, a = 11.49 Å, b = 5.75 Å, c = 7.49 Å, and β = 97.18°, the detailed atom positions are presented in Supplementary Table 1) can be applied to satisfactorily characterize the CuO x phase (Fig. 2b). To be specific, Supplementary Fig. 6 shows the high angle annular dark field (HAADF) and annular bright field (ABF) images of CuO along the same observation direction in Fig. 1d, i.e., Such OR is maintained when observed along different zone axes including ½112 CuO , ½100 CuO , and ½001 CuO axes (Supplementary Figs. 7-9), verifying that the nucleated phase possibly possesses an oxygen-deficient Cu 3 O 2 structure (compared to CuO). However, further experimental studies are of necessity to confirm the accurate value of x. This metastable CuO x phase is a distorted structure of CuO with O vacancies or Cu 2 O with O interstitials. Given that CuO x phase nucleates under strain and will slowly transform into CuO after the stress released, the local lattice distortion may exist which allows for~5% error in correlating the experimental and calculated results. It is worth mention that Cu 3 O 2 phase has been frequently reported during the oxidation of Cu and Cu 2 O 34,35 . Unfortunately, since Cu 3 O 2 is unstable and can be easily oxidized to CuO, its structural details remain mysterious due to the lack of atomic-scale structural investigation. The calculated X-ray diffraction (XRD) patterns based on current Cu 3 O 2 structural model and the experimental XRD pattern of pulsed laser deposited cuprous oxide thin films 36 are displayed in Supplementary Fig. 10. We found that although there might be some similarity between the two structures, the peaks do not match quite well between the two phases, possibly due to the strong texture in the experimental deposited film. Further efforts are required to reveal the structural relationship between current metastable CuO x phase and Cu 3 O 2 phase reported in the literatures [34][35][36] .
The nucleation of oxygen-deficient CuO x phase in CuO NW could be attributed to the Gorsky effect [10][11][12] , whereas the oxygen vacancies can diffuse from the tensile to compressive side under the inhomogeneous stress field induced by mechanical bending (Supplementary Fig. 3) 9 . Afterwards, removing the bending strain eliminates the stress gradient along the NW radial direction, resulting in the reversed movement of the oxygen vacancies and thus the transformation of CuO x phase back to CuO (Fig. 1d, e). The experimental results are repeatable when observed along ½101 CuO (Supplementary Fig. 11) and ½112 CuO ( Supplementary  Fig. 12) axes.
More importantly, the possible vacancy diffusion pathway is discussed. The time-lapsed images in Fig. 3a-c illustrate the evolution of phase boundaries between CuO x phase and CuO along ½011 CuO axis. It is evident that the boundaries mainly consist of ð111Þ CuO , ð111Þ CuO , ð200Þ CuO , and ð311Þ CuO planes (Fig. 3, Supplementary Fig. 4 and Supplementary Movie 3). The diffusion barriers for O vacancies in CuO were calculated through climbing image nudged elastic band (CI-NEB) method 37 . Three possible diffusion pathways with lowest barriers of 1.11, 1.11, and 1.89 eV are along ½110 CuO , ½110 CuO , and ½010 CuO directions, respectively (Fig. 3d), larger than the diffusion barrier of O vacancies near the surface along ½110 CuO direction (less than 1 eV) reported previously 37 . Accordingly, the structural model of CuO is presented in Fig. 3e, f to better illustrate the diffusion pathways. It is found that the diffusion directions of ½110 CuO , ½110 CuO , and ½010 CuO are located in the ð111Þ CuO , ð111Þ CuO , and ð200Þ CuO planes, respectively, suggesting that the appearance of the three planes as the dominant phase boundary can be well anticipated. Additionally, the ð311Þ CuO boundary can be considered as the combination of both ð111Þ CuO and ð200Þ CuO planes (Supplementary Fig. 13). In addition, according to the previous references 9 , the surface-mediated point defect could also occur under the mechanical stress. The CuO NW geometry is further investigated. We found that the NW cross-sections are nonsymmetric and not circular and surfaces are faceted ( Supplementary Fig. 14), which are consisted of various lattice planes, e.g., ð002Þ, ð110Þ, ð111Þ, and ð111Þ etc. Besides, the ð202Þ plane was reported to be another possible surface plane 38 . Hence, we have calculated the diffusion energy barriers of oxygen vacancies along different surfaces. The relatively lower calculated diffusion energy barriers of oxygen vacancies on different surface planes (e.g., ð002Þ, ð110Þ, ð111Þ, ð111Þ, ð202Þ, ð200Þ, ð011Þ, and ð112Þ) of CuO NW (less than 1 eV, Supplementary Fig. 15) than those in the bulk (the lowest migration energy in Fig. 3 is~1.11 eV) suggests that the oxygen vacancies prefer to migrate along the surface area, which may result in the relatively larger anelasticity in the nanosized material with higher aspect ratio.
It is generally believed that the room-temperature point defect diffusion in solids is limited, yielding a negligible effect on the mechanical behaviors. By contrast, the present experiments provide the direct evidence that the vacancy diffusion could indeed operate in nanomaterials, which could possibly result from enhanced surface-mediated diffusion and reduced vacancy migration energy under ultrahigh stress 9 . As shown in Supplementary Fig. 16, it is evident that the nonlinear Gorsky effect dominates during the anelastic strain recovery, identical to that reported in ZnO NWs 9 , suggesting that there are at least two kinds of point defects. Besides oxygen vacancy, Cu vacancy has been reported as another dominant type of point defect in CuO 39 . Considering the migration of both O and Cu vacancies, we obtained the average diffusivities of D 1 = 4.09 × 10 −14 cm 2 /s and D 2 = 3.39 × 10 −15 cm 2 /s for two types of point defects, respectively, close to the values reported for O vacancies and Zn interstitials 9 . Because the experimental NWs are not central-symmetric (Supplementary Fig. 14), and the stress/ strain is not evenly distributed along the NW length direction, the calculated values may not be accurate. Besides, the nucleation of oxygen-deficient CuO x phase implies that the O vacancy migration may play a major part. The averaged bending stress before the W tip removed is~1.29 GPa (Supplementary Fig. 17). Based on the previous investigation 7 , the e-beam induced temperature rise was estimated to be only 0.4 K. As compared with the high T m (~1600 K) of CuO, the thermal effect is negligible in mediating the anelasticity in single crystalline CuO NWs. Furthermore, the e-beam irradiation is shown to expedite the shape recovery when repeatedly compressing the same NW ( Supplementary Fig. 2). The momentum/energy transferred from the high-energy e-beam (~200 keV) to O atoms could facilitate the oxygen vacancy migration and thus accelerate the anelastic strain recovery 40 .
Similar anelastic deformation behavior was detected in twinned CuO NWs (Supplementary Figs. 18-19) 7 . The HRTEM images and inserted FFT patterns (Supplementary Figs. 18d-f) demonstrate the formation of CuO x phase, which gradually transformed back to CuO after stress release, implying that the point defect can get through a grain or interphase boundary 2 , similar to the intercrystalline Gorsky effect 41 .
The anelasticity induced by reversible phase transition was also found in Ni-Ti alloys 42 , whereas the lattice mismatch between two phases can contribute to the anelastic strain. Here, the shear strain induced by the nucleation of CuO x phase (central part in Fig. 4a) in original CuO NW is directly visualized and analyzed in the nanobridges fabricated by the top-down method 43 . Obviously, the shear strain slowly decreases with the gradual phase transition from CuO x phase to CuO (Fig. 4a-c). To describe the process quantitatively, the shear strain maps ε xy of the nanobridge are presented in Fig. 3d-f. The geometrical phase analysis (GPA) method is listed in Supplementary Fig. 20. The shear strain as large as 12% gradually decreases to 0 after the phase transition, accompanied with the nucleation and escape of dislocations ( Supplementary Fig. 21 and Supplementary Movie 4). The  Fig. 21a-c), consistent with the oxygen vacancy diffusion pathway calculated in Fig. 3.
The stress-mediated phase transition implies that during the bending process, the chemical bonds between Cu and O (Cu-O) are altered and the structure of CuO is distorted. The slight lattice distortion might affect the magnetic coupling between 3d Cu 2+ spins in Cu-O layers of superconductor Yttrium Barium Copper Oxide (YBCO) 44,45 , which plays a pivotal role in understanding the high-temperature superconductivity. For instance, the diffusion of O vacancies in Cu-O layers may also have impact on the superconductivity of YBCO 46,47 . Interestingly, our theoretical calculations ( Supplementary Fig. 22) indicate that Cu 3 O 2 is a half-metallic antiferromagnet, characterized by the spin-polarized electrons near the Fermi level, which may enable single spin superconductivity with triplet Cooper pairs 48 .
In summary, we present the first atomistic view of the phase transition from CuO to an oxygen-deficient metastable CuO x phase, as triggered by the stress-gradient-induced oxygen vacancy diffusion from the tensile to the compressive ends. After the stress releasing, the reversible phase transition from CuO x phase to CuO is directly monitored, leading to the gradual recovery of the anelastic strain. Meanwhile, three possible oxygen diffusion pathways along ½110 CuO , ½110 CuO , and ½010 CuO are proposed based on both experimental and theoretical studies. The existence of twin boundary does not shut off the anelastic behavior, implying that the oxygen vacancy could diffuse across the boundary. These findings provide the intuitive insight into the point defect-mediated mechanical behaviors in solid materials, consistent with that reported by Cheng et al. 9 . It is suggested that caution should be taken when interpreting the mechanical parameters of nanoscale metal oxides with high strength and inherent point defects when subjected to inhomogeneous stress field, such as bending and torque, etc.

Methods
Sample synthesis. The CuO NWs were prepared through thermal oxidation by heating copper grids/films at about 450°C for 1-2 h in a muffle furnace. Nanobridges were fabricated by traditional top-down method utilizing the focused ebeam 49 .
In situ TEM testing. The bending tests were performed on a Nanofactory EP1000 TEM-STM holder inside the TEM. The CuO NWs were attached to tungsten (W) rod with conductive silver paint, which served as one end of the in situ platform. A wedge-shaped W tip acted as the other end of the platform.
HRTEM and scanning TEM (STEM)/EELS experiments. In situ HRTEM observations were performed on JEOL F200 and JEOL JEM 2010FEF operated at 200 kV with e-beam intensity of 10-10 2 A/cm 2 . HAADF, ABF imaging and EDS, EELS analysis were carried out on JEOL ARM200CF operated at 200 kV, with current density on the scan region of around 10-10 2 A/cm 2 . The acquisition time for each selected pixel for acquiring EELS spectra is less than 1 sec to minimize the irradiation damage.
HAADF and ABF simulations. The HAADF and ABF images were simulated by QSTEM software. Based on current experimental conditions, the acceleration voltage of e-beam is set to be 200 kV, with spherical aberration of 0.001 mm, convergence angle of 15 mrad, and the sample thickness~5 nm.
Geometrical phase analysis. The GPA 50 was conducted to generate strain maps of HRTEM images. For the two-dimensional (2D) lattice shown in an HRTEM image, the tensorial distortion is defined as.
e ¼ e xx e xy e yx e yy whereas u = (u x , u y ) denotes the displacement field. In addition, the shear strain is usually defined as The analysis in this work was done by open-source software Strain + +. The details including nonlinear g vectors used for GPA are presented in Supplementary  Fig. 20.
Simulation details. First-principles calculations were carried out using the Vienna ab initio simulation package (VASP) 51 , with the projector augmented wave method 52,53 and the Perdew-Burke-Ernzerhof (PBE) 54 exchange-correlation functionals. A 450-eV energy cutoff and a U eff of 7 eV in the PBE + U method were used throughout the calculations. ATAT 33 was used to automate first-principles phase diagram calculations to find possible CuO x phases. The Monkhorst-Pack scheme of k-point mesh was chosen such that the number of k-points times the number of atoms in the unit cell being 1000, which keeps the density of k-point constant regardless of supercell size.
Calculation and discussion of the bending strain in CuO NW. The bending strain ε in a bent NW can be calculated by the formula where d is the diameter of the curved NW, ρ is the NW's curvature radius, and κ is the curvature. To calculate the strain in the NW, the NW's shape should be fitted into a mathematical curve by polynomial fitting with the curvilinear equation y ¼ f ðxÞ. Then the curvature can be calculated by the formula.
κ ¼ jy00j where y 0 ¼ f 0 ðxÞ and y 00 ¼ f 00 ðxÞ, which represent the first and second derivative of y ¼ f ðxÞ, respectively.
Calculation of diffusivities of point defects in CuO NW. According to the Gorsky effect or nonlinear Gorsky effect, the diffusivity of point defects could be estimated by measuring the relationship between strain and time as well as considering the geometry of NWs. The relationship of the anelastic strain and time is approximately described by an exponential law in the Gorsky relaxation process. The logarithm transform of anelastic strain would be related to time linearly, with the slope being 1/τ (the relaxation time τ). For cylindrical specimens with the diameter of d, the diffusivity D is related to the relaxation time τ by 12 13: Take the NW shown in Fig. 1b for an example (d~46 nm), we obtain the average diffusivities of D 1 = 4.09 × 10 −14 cm 2 /s and D 2 = 3.39 × 10 −15 cm 2 /s.