Twinning-assisted dynamic adjustment of grain boundary mobility

Grain boundary (GB) plasticity dominates the mechanical behaviours of nanocrystalline materials. Under mechanical loading, GB configuration and its local deformation geometry change dynamically with the deformation; the dynamic variation of GB deformability, however, remains largely elusive, especially regarding its relation with the frequently-observed GB-associated deformation twins in nanocrystalline materials. Attention here is focused on the GB dynamics in metallic nanocrystals, by means of well-designed in situ nanomechanical testing integrated with molecular dynamics simulations. GBs with low mobility are found to dynamically adjust their configurations and local deformation geometries via crystallographic twinning, which instantly changes the GB dynamics and enhances the GB mobility. This self-adjust twin-assisted GB dynamics is found common in a wide range of face-centred cubic nanocrystalline metals under different deformation conditions. These findings enrich our understanding of GB-mediated plasticity, especially the dynamic behaviour of GBs, and bear practical implication for developing high performance nanocrystalline materials through interface engineering.


Supplementary Fig. 5 Atomic von Mises stress contours showing evident stress accumulation and release before and after the deformation twinning, respectively.
The calculation of the atomic von Mises stress is described in the Methods. The colour is assigned to each atom according to its value of atomic stress. (a, d) Before deformation twinning, severe stress accumulation occurred at GB. (b, e) Surfaceactivated twin released the local stress accumulation. (c, f) Full twinning induced evident stress reduction at GB. All scale bars: 5 nm. Supplementary Fig. 6 Twinning tendency governed GB deformation. (a) GB energy increased after the dynamic structure adjustment for a GB with TT = 2.9. (b) GB energy decreased after the dynamic structure adjustment for another GB with TT = 1.3. (c) Twinning was absent for a GB with insufficient twinning tendency TT = 0.82. The misorientation and inclination angles are marked at the bottom right of the GB, while the calculated GB energies before and after the twinning-assisted GB adjustment are given at the bottom of the sample. All scale bars: 5 nm. Supplementary Fig. 7 MD simulation of the dynamic adjustment of an 87° <110> tilt GB assisted by twinning. (a) The initial atomic structure of the simulated bicrystal with the same GB1-2 misorientation and inclination as that in the experiment (Fig. 4g). Supplementary Fig. 9 The twinning-assisted variation in shear coupling factor of GBs in nanocrystalline FCC metals (summarized in Fig. 5i). The determination for the misorientation and inclination of the original GB1-2 is described in Supplementary Discussion 4. MD simulations were performed on GB1-2 and the corresponding GBT-2 to calculate the shear coupling factors using the same model as that in Fig. 3a. The shear coupling factor of GBT-2 was estimated to be universally lower than GB1-2, indicating an enhanced shear deformability due to deformation twinning.
for GB1-2 and GBT-2 can therefore be theoretically predicted by the following formulas: (1) Following these equations, we plotted the shear coupling factors as a function of the misorientation angle, , in Supplementary Fig. 3. Substituting the misorientation angles of GB1-2 ( = 23°) and GBT-2 ( = 47°) into these equations, the magnitude of the theoretical shear coupling factor of GBT-2 ( = 0.87) was found to be smaller than that of GB1-2 ( = -1.32), confirming that GBT-2 would migrate a larger distance under the same shearing displacement. We summarized the shear coupling factors obtained from theoretical model, MD simulations and experiments in Supplementary Table 1.

Supplementary Discussion 2: Energy-based elastic driving force for GB migration
As shown in the inset of Fig. 3c, given that a uniaxial tension loading (i.e., a normal strain ) was applied to the bicrystal to simulate the twinning-assisted dynamic adjustment of GB mobility, which also imposes a biaxial strain state (ε xx and ε yy ) in the GB plane (denoted as x-y plane in the following derivation) in order to ensure a steady-state migration without any GB sliding since all resolved shear stresses on the GB plane are zero. We can calculate the corresponding stress components following the Hooke's law: σ xx = C 11 ε xx + C 12 ε yy + C 13 ε zz (3) σ yy = C 21 ε xx + C 22 ε yy + C 23 ε zz (4) σ zz = C 31 ε xx + C 32 ε yy + C 33 ε zz (5) where the elastic constants can be easily determined using MD simulations. In specific, we applied a finite strain component and measured the variation of the stress tensor, thereby getting the elastic constant matrix. The stored elastic energy density can be written as: The GB migration velocity can be expressed as v = MP, with M and P being the GB mobility and the driving force, respectively. The driving force P can be calculated as P = F + -F -, where F + and − are the elastic energies in the upper and lower grains across the GB, respectively. In our MD simulations, the elastic energy densities of the three single crystalline grains (i.e., G1, G2 and Twin in Fig. 3c) were estimated to be F G1 = 40.89ε 2 , F G2 = 100.75ε 2 , and F Twin = 19.79ε 2 , respectively. One then arrived at the driving force P = 59.86ε 2 for GB1-2 and P = 80.96ε 2 for GBT-2.

Supplementary Discussion 3: Critical twinning tendency
As proposed in a previous study by Kim et al 3 , the critical stress required to generate partial dislocations can be derived as where ∆γ i is the energy barrier for the formation of partials, b p is the Burgers vector along the slip direction, G is the shear modulus, R is the radius of sample, v is the Poisson's ratio, α is a correction factor (~0.5), and r 0 is the core cut-off radius of the dislocation. The energy barrier for the formation of twinning partials and trailing partials can be derived as ∆γ tw = γ utf -γ sf and ∆γ tr = γ usf -γ sf . They can be obtained from the generalized stacking fault energy curve 4 . Following this method, the critical twinning tendency was calculated to be 0.93 for Au.

GBs among different nanocrystalline metals
Numerous observations of parallel or oblique intersections of GBs and TBs were reported in nanocrystalline metals, with a wide range of misorientations and grain sizes.
Unlike in bicrystals, GBs in nanocrystalline metals are usually pinned by the GB/TB junctions, so that their self-adjustments are frequently triggered to accommodate the local plasticity. In nanocrystalline with complex GBs networks, deformation twinning is frequently associated with GBs, and is probably formed by the self-stimulated adjustment of GB structure. As a result, GB crystallography adjustment can be identified based on a simple geometric analysis of the resultant GB structure after the designated deformation twinning. When a LAGB (misorientation was less than 16°) composed of highly mobile dislocations is intersected with a TB, the transformation was likely to start from an immobile HAGB (misorientation exceeded 16) to a mobile LAGB 5,6 . If two GBs at the GB-TB junction were both HAGBs, the original GB is assumed to have a smaller intersection angle with respect to the TB as compared with the newly formed GB 7,8,9,10,11 . If the GBs are not pinned by the TB, meaning that the original GB was fully transformed 12,13,14 , we thereby determined the original GB structure based on the twin geometry. Fig. 5i summarized these in situ and ex situ experimental results associated with the self-driven twinning induced GB adjustment, in samples obtained by different methods.