Non-destructive detection of cross-sectional strain and defect structure in an individual Ag five-fold twinned nanowire by 3D electron diffraction mapping

Coherent x-ray diffraction investigations on Ag five-fold twinned nanowires (FTNWs) have drawn controversial conclusions concerning whether the intrinsic 7.35° angular gap could be compensated homogeneously through phase transformation or inhomogeneously by forming disclination strain field. In those studies, the x-ray techniques only provided an ensemble average of the structural information from all the Ag nanowires. Here, using three-dimensional (3D) electron diffraction mapping approach, we non-destructively explore the cross-sectional strain and the related strain-relief defect structures of an individual Ag FTNW with diameter about 30 nm. The quantitative analysis of the fine structure of intensity distribution combining with kinematic electron diffraction simulation confirms that for such a Ag FTNW, the intrinsic 7.35° angular deficiency results in an inhomogeneous strain field within each single crystalline segment consistent with the disclination model of stress-relief. Moreover, the five crystalline segments are found to be strained differently. Modeling analysis in combination with system energy calculation further indicates that the elastic strain energy within some crystalline segments, could be partially relieved by the creation of stacking fault layers near the twin boundaries. Our study demonstrates that 3D electron diffraction mapping is a powerful tool for the cross-sectional strain analysis of complex 1D nanostructures.


S1. Five-fold twinned structure identification of the Ag nanowires by axial rotation electron diffraction.
Axial rotation electron diffraction has been employed to identify the internal twinning structure of the Ag nanowires in this study and clearly reveals the five-fold twinning structure in the nanowires. The twinning structure is identified as five identical face-centered cubic (FCC) single crystalline segments sharing a common [110] axis and joined at {111} twinned plane cyclically.   diffraction center. In the Ω  plane the deviation of the diffraction center of (331) FCT reflection from that of (331) FCC reflection is 0.02 nm -1 along the direction parallel vector.
To investigate the influence of the phase transformation on the (331) intensity distribution, we build the structural model of Ag single crystalline segment with FCT core and FCC sheath, and simulate the corresponding intensity map of (331) reflection in the Ω plane.

S3.Star-disclination strain field
Assuming an infinitely long isotropic cylinder with a wedge disclination axis, the disclination core induces a strain field perpendicular to the disclination axis, the corresponding atomic displacement in cylindrical coordinates, r and φ, can be expressed as followings. 2 Here, R is the radius of the cylinder, Θ is the characteristic rotation angle of the disclination, and ν is Poisson's ratio. For FCC silver five-fold twinned structure, the rotation angle Θ is  g v

S6. Round corner effect (shape effect)
The ideal model for Ag FTNWs exhibits a pentagonal cross-section bounded by five (001) surfaces. But some cross-sectional TEM observations have identified a morphology with round corners slightly deviated from the pentagonal cross-section. 1,4 Considering this situation, we have built a cross-sectional atomic configuration for a Ag single crystalline segment with round corners as shown in Fig. S7(b). In this configuration, the atomic lattice distortion is simulated by the star-disclination model. For comparison, the atomic structural model of a single crystalline segment for an ideal case of Ag pentagonal nanowire with star-disclination strain distribution has shown in Fig. S7(a). In Fig. S7 In addition, for profile, the subsidiary peak intensity for round corner structural model is relatively weak, as indicated by arrow in Fig. S7(c). The intensity for this subsidiary peak is less than 5% of the maximum of (331) diffraction center as shown in Fig. S7(c). As the limitation of SNR (signal to noise ratio) for our currently used CCD detector, such weak subsidiary peaks cannot been detected. These comparison results 002 g v   Fig. S8(a) illustrates the diffraction geometry for the structural analysis of Ag FTNW with diameter of 30nm in this study. To evaluate the electron diffraction dynamic effect in our study case, here we suppose that the (331) diffracted beam when passing through the Ag nanowire is multiply scattered by assuming its transmitted intensity correlated with the projection thickness of the Ag nanowire [ Fig. S8(b,c)]. In this simulation, we use the pure star-disclination model to build the atomic configuration of the Ag FTNW with diameter of 30nm schematically viewed in Fig. S4(b). According to the orientation relationship between the incident electron beam (EB) and the nanowire illustrated in Fig. S8(a), the simulated (331) intensity distribution of T1~T5 segment is shown in Fig. S8(d) and (e) which corresponding to the (331) beam intensity distribution below the nanowire demonstrated in Fig. S8(b) and (c), respectively.

S7. Dynamic (Multiple Scattering) effect evaluation
The simulation results indicate that the multiple scattering of the electron beam affects the symmetric characteristics of (331) reflection diffracted from the single crystalline segments of T2~T5. Because that T1 is mirror-symmetric about the tilting axis, such symmetric feature is maintained by its (331) reflection without the influence by the electron dynamic effect. But g v 14 shown in Fig. S8(h) are all less than the expected value for the pure star-disclination model in the kinematic approximation, and some ratios are even decreased by more than 20%.
Moreover, the dynamic calculation results shown in Fig. S8(d) and (e) also reveal that the intensity map containing five (331) reflections in the Ω plane exhibits a mirror-symmetric feature about the tilting axis indicated by the red dashed line. That reflects the real space symmetry between the electron beam and the Ag nanowire schematically shown in Fig. S8(a).
As a result, such symmetric feature is also shown in the calculated integrated intensity ratios (I 2 /I 1 as defined in the main text, Fig. 5  On the basis of star-disclination atomic configuration for the single crystalline segment, we introduce one atomic layer of stacking fault parallel to a {111} twin plane of the segment.
This operation changes the regular close packing, …ABCABC…, to the packing sequence of …ABCBABC…,schematically displayed in Fig.S9(a). According to this atomic configuration, we have simulated a series of 2D intensity distribution map for (331) reflection by varying the distance between the stacking fault layer and the parallel twin plane (indicated as d in Fig.S9(a)). In Fig.S9(b-c), we present the color map of (331) intensity line-profile varying with the distance between the stacking fault layer and the twin plane. The original point for the deviation vectors is set as the (331) diffraction center for the ideal Ag segment model without lattice distortion and defects [ Fig. 4(a)]. The simulated results shown in Fig.S9(b-c), clearly indicate that the intensity fine structure variation due to the introduction of stacking fault strongly depends on the location of the stacking fault layer.
Kinematic simulation for the pure star-disclination model evidently shows that the intensity streaking along direction is stronger than that along the opposite direction (i.e.  diffraction spot splitting can be observed, while the distance of stacking faul layer to its parallel twin place is in the range from about 2nm to 6nm. As the distance is in the range from about 6nm to 10nm, the intensity streaking of (331) reflection towards 1 1 1 g v direction is more evident with respect to the opposite direction. But in the case that the stacking fault layer is close to the triangular corner (i.e. d > 10nm) as shown in Fig. S9(c, d), the (331) reflection also exhibits more intensive flare in the direction with respect to the opposite direction, similarly to the pure star-disclination model but with the diference that a weak subsidiary peak possibly apears along the direction. In Fig. S9(b, c) it also can been found that if the stacking fault layer is next to its parallel twin plane (d<2nm), the intensity The 30nm diameter of the nanowire is measured from Fig. 2(a). In Fig. 2(a) the nanowire shows a mirror-symmetric contrast about the long axis which corresponding to the symmetric orientation of the nanowire's cross-section with respect to the incident electron beam (EB) as shown in this figure.