Dislocation mechanisms and 3D twin architectures generate exceptional strength-ductility-toughness combination in CrCoNi medium-entropy alloy

Combinations of high strength and ductility are hard to attain in metals. Exceptions include materials exhibiting twinning-induced plasticity. To understand how the strength-ductility trade-off can be defeated, we apply in situ, and aberration-corrected scanning, transmission electron microscopy to examine deformation mechanisms in the medium-entropy alloy CrCoNi that exhibits one of the highest combinations of strength, ductility and toughness on record. Ab initio modelling suggests that it has negative stacking-fault energy at 0K and high propensity for twinning. With deformation we find that a three-dimensional (3D) hierarchical twin network forms from the activation of three twinning systems. This serves a dual function: conventional twin-boundary (TB) strengthening from blockage of dislocations impinging on TBs, coupled with the 3D twin network which offers pathways for dislocation glide along, and cross-slip between, intersecting TB-matrix interfaces. The stable twin architecture is not disrupted by interfacial dislocation glide, serving as a continuous source of strength, ductility and toughness.

S trength and ductility (and hence toughness) are key mechanical properties of structural materials [1][2][3][4][5][6][7][8][9][10][11][12][13][14] , although these properties are often mutually exclusive 15 . In crystalline metallic materials, strength and ductility depend on the presence of crystal defects and how they move under mechanical loading. Dislocations serve as the prime carrier of plasticity in metals and their motion to create plastic deformation is strongly influenced by interactions with other dislocations as well as defects such as solute atoms 14,[16][17][18][19][20] , stacking faults 21,22 , grain boundaries (GBs) [23][24][25] and reinforcement particles or precipitates 26,27 . In general, strong interactions (obstacles) strengthen a material although this often limits its ability to plastically deform. Twinning, however, appears to be a deformation mechanism capable of defeating this 'conflict' between strength and ductility [1][2][3][4][5][6]8,9,16,28,29 . The presence of twins usually serves to impede dislocation motion and induce strengthening, but multiple twinning systems can also enhance ductility. This is apparent in twinning-induced plasticity (TWIP) steels, which are known to form multiple types of twins that result in high strength with substantial uniform ductility 6,10-12 . Another notable example includes certain equiatomic multielement alloys, termed high-entropy alloys 30 (HEAs), based on the CrMnFeCoNi composition that have a single-phase facecentered cubic structure (fcc) structure 31,32 with relatively low-stacking-fault energies (SFEs), comparable with 304 stainless steels 33 and relatively large separations between the Shockley partials 34 . These alloys can display excellent strength 9,35 , ductility 9,35 and toughness 1 at room temperature, properties which are further enhanced or maintained at cryogenic temperatures where deformation nano-twinning becomes a more prominent mode of deformation. Despite our recent observations of various toughening mechanisms occurring on the nanometre length-scale in the vicinity of a crack tip in such an alloy 8 , the quantitative strengthening effect from deformation twinning and the nature of twinning-induced plasticity remain somewhat uncertain.
In this work, we show that the mechanical behaviour of the nominally equiatomic alloy CrCoNi, a medium-entropy alloy (MEA) with a single-phase, fcc structure 16,36 , and even better mechanical properties than the CrMnFeCoNi high-entropy alloy-specifically, a high strength (B1 GPa) and ductility (B60% uniform elongation) combined with exceptional fracture toughness (K Ic 4200 MPaOm) 8,16 -can be related to its capacity for twinning-controlled deformation. Our ab initio calculations based on the density-functional theory (DFT) suggest that this alloy has a negative SFE at 0 K, similar to what has been reported for some other systems [37][38][39][40][41] and high propensity for twinning when compared with pure fcc metals 42 . We seek to demonstrate that a 3D twin network is formed within the grains of this fcc CrCoNi MEA and that the interactions of dislocations with these twins can lead to a simultaneous increase of strength and ductility, that is, to identify the origin of its excellent mechanical properties.

Results
Numerical simulations. DFT-based ab initio calculations were performed to compute the formation energy of the equiatomic CrCoNi alloy with different crystal structures as well as their planar fault energies. In previous theoretical work 33,43,44 , the formation energies of medium-and high-entropy alloys were treated with the coherent potential approximation (CPA) 44,45 or the special quasi-random structure (SQS) 46 method in conjunction with ab initio treatments. In this study, the formation energies of CrCoNi crystals were explicitly assessed with the 'multiple randomly populated supercell' approach. The configurational dependence of the formation energy of CrCoNi MEAs is shown in Supplementary Fig. 1. In our calculations, atoms of the different elements comprising the MEA were randomly assigned to the lattice points of the corresponding crystal structure, followed by geometrical optimization to obtain the ground state configuration of each structure. Although computationally demanding, this approach gives us an advantage by allowing direct evaluation of the stacking-fault energies and their formation energy barriers.
Supplementary Table 1 lists the formation energies of hypothetical face-centered cubic (fcc), hexagonal close-packed (hcp), double hcp (dhcp) and 9R structures for the CrCoNi alloy. Note that their respective stacking sequences are: fcc-yABC ABCy, hcp-yAB ABy, dhcp-yABAC y and 9R-yABA BCB CACy It was found that the formation energy of hcp CrCoNi at 0 K is slightly lower than that of fcc CrCoNi, which implies that the hcp structure can be a competing phase during the synthesis of CrCoNi ( Supplementary Fig. 1). The energy difference at 0 K between fcc and hcp CrCoNi was found to be B7 meV per atom (that is, 0.68 kJ mol À 1 ). According to our free-energy calculations based on the quasi-harmonic approximation ( Supplementary Fig. 2), the fcc structure gains a free-energy advantage at higher temperatures (for example, 500 K), due mainly to the contribution from lattice vibration. Similar results (namely that hcp is stable at low temperatures and fcc at higher temperatures) were obtained recently for the 5-element HEA, CrMnFeCoNi, when, in addition to configurational entropy, other entropic contributions including electronic, vibrational and magnetic were included in the total energy calculations 44 . Lattice distortions arising from size mismatches of the constituent atoms in the CrCoNi MEA with the fcc or hcp structure were also examined from the atomic pair-distribution functions (PDFs) of CrCoNi crystals; these PDFs of fcc and hcp CrCoNi at 0 K are shown in Supplementary Fig. 3. Further description of the analyses is provided in Supplementary Note 1.
The stacking faults in fcc CrCoNi were analysed with ab initio modelling; results are shown in Fig. 1. A slab of CrCoNi with the fcc structure (360 atoms) was first created by sequentially stacking 12 close-packed (111) atomic planes. The slabs have two free surfaces. In the simulation cell, in the direction perpendicular to the slab (z direction), a vacuum of thickness 1.6 nm is inserted between slabs to separate each slab from the adjoining ones in the next periodic cell (to minimize the interactions of the slabs). The atomic configurations of the slab were geometrically relaxed in the three directions. Next, an intrinsic stacking fault, of energy g isf , was created by shifting the top six layers along the 11 2 h i direction by the Burgers vector of the Shockley partial b s ¼ a 6 11 2 h i , where a is the lattice parameter; this resulted in a stacking sequence: ABCABC|BCABCA, shown in Fig. 1b. The stacking-fault energy is obtained by the energy difference of the two optimized structures normalized by the area of the stacking fault A.
Subsequent displacement of the top five layers in Fig. 1b along the 11 2 h i direction results in a two-layer stacking fault (Fig. 1c), which is called an extrinsic stacking fault (ABCABC|B|ABCAB). Further shifting of the fault in Fig. 1c leads to a three-layer fault, shown in Fig. 1d and so on. As such, continued shifting of the crystal will create a twinned structure with a twin boundary. The calculated energies of the intrinsic stacking fault, g isf , and twin boundary, g TB , are given in Table 1. The energy g us is that of the unstable stacking fault, and g ut is the nucleation energy barrier for the formation of twin boundaries (Fig. 1f).
Alternatively, stacking-fault energies can be calculated through the use of a parametrized method, that is, the axial interaction model (AIM) 47 . Using AIM, the energy of an intrinsic stacking fault can be expressed in terms of the energies (E) of the various structures and the fault areas (A) as: Substituting the values of the formation energies of the hcp, fcc and dhcp structures from Supplementary Table 1, we obtain g isf ¼ À 23 mJ m À 2 , g esf ¼ À 20 mJ m À 2 and g TB ¼ À 10 mJ m À 2 , respectively, which are generally consistent with the results of our explicit calculations provided in Table 1.
An energy barrier must be overcome when an intrinsic stacking fault is created by displacing the upper half of the crystal, as demonstrated in Fig. 1f. This energy barrier corresponds to the unstable stacking-fault energy of fcc CrCoNi, g us . On further displacement of the crystal with a pre-existing fault (as shown in Fig. 1b), another energy barrier is crossed, namely g ut , the energy barrier for twin-boundary formation. These energy barriers lie on the minimum energy paths between the stacking faults, and have profound implications for the deformation mechanism of the crystal.
In this work, we used the nudged-elastic band (NEB) method 48 in the DFT calculation to obtain the unstable stackingfault energies along the deformation paths. During the NEB simulation, the atoms are relaxed to the minimum energy paths. It should be mentioned that, without the atomic relaxation process, the unstable fault energy calculated for the rigidly shifted crystal is about 1.5-2 times higher than the correct values shown in Fig. 1f.
Having obtained the stacking-fault energy values in Fig. 1f, we are able to evaluate the propensity of twinning ('twinnability') in the CrCoNi crystal. On the basis of Tadmor and Bernstein's work on fcc metals 42,49 , an empirical expression for twinnability, t ta , is: Using this equation, the dimensionless twinnability for the present CrCoNi fcc alloy is t ta ¼ 1.07 ± 0.02, which is higher than that of all pure fcc metals 42 (for example, the numerically derived t ta for Ag is B1.05), and comparable to that of Fe-Cr-Ni TWIP steels 50 (1.08-1.12, based on equation (2) and the ab initio data from ref. 50). The high propensity for twinning of fcc CrCoNi appears to be a factor in the excellent strength, ductility and toughness of this MEA.
Nanostructural characterization. This calculated twinnability is consistent with the twinning observed in the CrCoNi alloy after plastic deformation 8 . To examine its specific atomic-scale mechanisms of deformation, we performed advanced structure characterization utilizing quantitative in situ transmission along the pathway 1 6 11 2 is given by the magnitude of the Burgers vector of a Shockley partial dislocation, b s . Here, g isf and g esf represent the stacking-fault energies of intrinsic (b) and extrinsic (c) stacking faults, respectively. g us is the unstable stacking-fault energy, and g ut denotes the energy barrier for the formation of the initial twin boundary. After g ut is overcome, the subsequent energy barriers (for example, g 0 ut ) for creating multi-layer twins are smaller than g ut . The energy barriers along the displacement pathway were obtained with the nudged-elastic band method in our ab initio calculations. ARTICLE electron microscopy (TEM) and aberration-corrected scanning transmission electron microscopy (STEM). We also performed quantitative in situ TEM compression tests to investigate the strengthening effect of a twin boundary in the CrCoNi alloy. By compressing micro-pillars with and without a twin boundary, we were able to quantify the strengthening effect from blocked dislocations at a twin boundary (TB). The dislocation-twin and twin-twin interactions during plastic deformation were systematically studied in situ in the TEM to reveal the influence of the 3D twin architecture on the plastic deformation of the material. Remarkably, while the twin boundaries contributed to strengthening by acting as barriers to dislocation motion, the interconnected twin boundaries in the 3D twin network can also generate significant ductility by offering multiple pathways for dislocation motion along the twin boundaries. Post-mortem TEM investigations of the CrCoNi samples revealed that large numbers of deformation twinning events occurred in samples deformed in uniaxial tension; three twinning systems were activated within individual coarse grains, forming a 3D twin architecture in which multiple twins with different thicknesses form and intersect each other. The twins typically had thicknesses ranging from B100 nm to several micrometres (examples are shown in Fig. 2a), and were present within most grains that we examined. Two twin variants, comprising a compound twin structure that is common in fcc crystals, were observed to intersect each other; these are labelled as 'Twin 1' and 'Twin 2' in Fig. 2a. Selected area electron diffraction (SAED) patterns taken along the [110] zone axis (Fig. 2c) reveal separate sets of spots, belonging to the matrix and the twin, respectively. Two types of twin boundaries were observed: P 3 f111g coherent twin boundaries (CTBs) and P 3 f112g incoherent twin boundaries (ITBs). Dislocations interact with these TBs in various ways. For example, dislocations pile-up at CTBs when they glide on a {111} plane that is not parallel to the CTB, as shown in Fig. 2a. Moreover, dislocation arrays can also form near the TBs, either at a CTB or the intersections of CTBs and ITBs (Fig. 2b). Corresponding atomic structures of a dislocation at the intersection of a CTB {111} and ITB {112} are shown in Fig. 2d, which is a typical high-angle annular dark field (HAADF) STEM image obtained in the aberration-corrected TEAM0.5 TEM microscope operating at 200 kV. A 9R structure composed of a set of Shockley partial dislocations with a repetitive sequence b2:b1:b3 (refs 51-54) on every (111) plane can be seen in the {112} ITB. The twin architecture is presumably formed due to twin-twin interactions. A smaller twin (for example, Twin 3 in Fig. 2) can be generated within large parent twins by the ITB of other twins (Twin 1) advancing and hitting the CTB of a thick twin (Twin 2) during plastic deformation, as shown in Fig. 2.
In situ mechanical testing. A high density of twins is expected to have a marked strengthening effect as twin boundaries can act as effective barriers to dislocation motion. Using micro-pillar compression experiments, we attempted to quantify the contribution of an individual twin boundary to the strength of this CrCoNi alloy. We used B300-nm diameter, focused-ion beam (FIB) machined micro-pillars, which were tested in a JEOL 3010 TEM at 300 kV, either with or without a {111} twin boundary (and no other boundary), as shown respectively in the dark field images in Fig. 3a,b and in the Supplementary Movie 1. The SAED pattern in the inset of Fig. 3a shows two sets of spots, confirming the existence of the twin. Engineering stressdisplacement curves from the compression of these pillars (Fig. 3c) clearly show the much higher strength of the pillar containing an initial twin. Specifically, the maximum strength of the pillar with a pre-existing twin exceeded 2.5 GPa, that is, about 1 GPa higher than that without a twin. As the sizes of the pillars were kept the same to minimize possible size effects, such an elevation in strength can be plausibly attributed to the presence of the twin boundary. However, as these nano-pillar tests only investigate limited volumes, in situ TEM straining tests were also performed to systematically investigate the dislocation-twin and twin-twin interactions, with particular focus on the formation of the 3D twin architecture and how this architecture influences the dislocation activity.
The in situ straining experiments enabled direct observations of the formation of the twinning architecture and the interactions between dislocations and twin boundaries, as shown in Fig. 4 and Supplementary Movies 2-5. During straining, multiple types of deformation twins were quickly activated, forming a hierarchical architecture consisting of twins with different thicknesses. Figure 4a shows the dynamic formation of two twins, labelled as 'Twin 1' and 'Twin 2', and their interaction to form a twin junction. It was observed that the twins propagated very fast until they hit the boundary of other twins. During further straining, the hierarchical twin architecture remains stable with no noticeable thickening or de-twinning. Activity of screw dislocations was also observed at the TB. A dislocation, originally gliding on the boundary between 'Twin 2' and the matrix, can be seen to impinge at the intersection of 'Twin 1' and 'Twin 2', before subsequently cross-slipping onto the boundary between 'Twin 1' and the matrix, on another {111} plane. From the real-time observations, the twin boundaries clearly act as strong barriers to dislocation motion, preventing dislocations from moving across them and resulting in the pile-up of dislocations (Supplementary Movie 3), as has also been reported previously [55][56][57][58][59] . Although impeding dislocation motion usually compromises ductility, the generation of multiple types of deformation twins contributes to the homogeneous plastic deformation. More importantly, the intersected boundaries of the hierarchical twins in the CrCoNi MEA were able to serve as fast channels for dislocation movement. Specifically, dislocations can cross-slip from one twin boundary to another using the 'overpass' constructed by the intersected twin boundaries, resulting in a more homogeneous distribution of dislocation activity in three dimensions. Although we did not capture the detailed process, sessile dislocation(s) should be involved in the cross-slip phenomenon of those imperfect dislocations at the intersection of the twin planes. We observed that, during further straining, the majority of the deformation inside individual grains occurred through gliding of dislocations along the twin boundaries in the 3D architecture. The dislocations moved fast along the boundaries, which is consistent with previous reports that demonstrated that the dislocation motion on a twin boundary would be faster than that in the matrix since the impediment from the image force is null if the Burgers vector of dislocations is parallel to the twin boundary 41,60,61 . Figure 4b shows a side view of a twin boundary in which the TBs are inclined and intersect both the top and bottom surfaces of the TEM film. Although cross-slip of partial dislocations 62,63 at twin-twin junctions could not be fully observed due to the limited time-resolution of in situ TEM, in Fig. 4b we show the glissile boundary dislocations with Burgers vector parallel to o1124 gliding on the twin boundary; however, the twin boundaries remained stable as these dislocations moved along them, that is, there was no evidence of either twin growth or de-twinning occurring during such deformation (Fig. 4b and Supplementary Movies 4 and 5). As such, a high ductility was achieved.

Discussion
On the basis of the in situ straining of the CrCoNi, we have found that a three-dimensional hierarchical twin network is established within individual grains in this MEA, associated with its very low (negative) stacking-fault energy calculated at 0 K; this network presents substantial barriers for dislocation motion, and contributes to its high strength and significant strain hardening. However, at the same time, the network provides multiple pathways for the easy motion of dislocations, which permits the simultaneous generation of significant plastic deformation. Importantly, the formation of the 3D twin network is achieved within relatively large grains (B5-50 mm in size 8 ), and is found to be stable against de-twinning as deformation continues with the twin-boundary interfaces serving as pathways for dislocation slip. This observation is significantly different from that previously reported in twinning-deformation dominated materials 3,4,6,7,64 . As a result, high strength coupled with high ductility and continuous strain hardening is achieved in this alloy, which presents the perfect ingredients for its exceptionally high fracture toughness 8 . As lower (cryogenic) temperatures serve to elevate the strength and hence are expected to further promote twinning activity, the damage tolerance (strength with toughness) of this alloy is destined to be enhanced at such low temperatures, which is exactly what has been observed experimentally 8 . This dual effect on dislocation activity is a consequence of the three-dimensional hierarchical twinning architecture that is generated with plastic strain, which in turn results from the high twinnability of this particular alloy.
We note that 3D twinning networks resulting from the activation of three twinning systems may also form within individual grains in TWIP steels, specifically under complex loading conditions such as torsion. The formation of a high density of twin lamellae serves to refine the grains, thereby hindering dislocation motion and generating strain hardening; ductility is considered to originate from the formation of the deformation twins. In comparison, the density of twins in CrCoNi is much lower, but the intersected twin boundaries of different twins act to construct an overpass, which enables fast motion of dislocations on the boundaries and cross-slip from one boundary to another, leading to more homogeneous plastic deformation even within individual grains. We believe that documentation of the enhanced twinninginduced toughness of this MEA may serve not only to improve our understanding of the extraordinary structural behaviour of specific high-/MEAs but also to present new directions for the future design of metallic alloys with unprecedented combinations of mechanical properties.

Methods
Materials preparation and microstructural characterization. Samples for this study were extracted from a previously produced nominally equiatomic CrCoNi MEA whose microstructure and mechanical properties were reported in a recent paper 8 where details of its processing and mechanical characterization can be found. Atomic structures were investigated using the aberration-corrected TEAM0.5 transmission electron microscope (operating at 200 kV), housed at the National Center for Electron Microscopy at the Lawrence Berkeley National Laboratory (LBNL), and the in situ compression tests were performed using a Hysitron PI95 nanoindenter in a JEOL 3010 microscope at 300 KV. The nanopillars for the in situ compression tests were produced using focused-ion beam techniques; details of sample preparation and in situ compression have been described in previous studies 65,66 . The in situ TEM tensile tests were conducted at room temperature using a Gatan model 654 single-tilt straining holder in an FEI Tecnai G2 F20 TEM operating at 200 kV. Roughly 12 samples, thinned by jet polishing and well attached to the substrate, were selected for in situ tensile straining and detailed TEM investigation as described in a previous paper 22 . Time-resolved TEM and HRTEM images of the regions of interest were recorded with a Gatan CCD camera at 10 frames per second.
Computational methods. Ab initio calculations were performed with the plane-wave based Vienna Ab initio Simulation Package (VASP) 67,68 . The valence electrons of Cr, Co and Ni are, respectively, 6, 9, 10 in the calculation and the projector augmented wave (PAW) method 69 was used for the pseudo-potential treatment of core and semi-core electrons. In our calculation, the crystal structures, with periodic boundary conditions, typically contain 300-500 atoms, depending on the specific crystal structure. Atoms are randomly assigned to the lattice points of the corresponding crystal structure, followed by geometrical optimization to obtain the ground state configuration of each structure. The formation energy of each structure corresponds to a statistical mean of 80 such calculations. The Purdew-Wang-type generalized gradient approximation (GGA) 70 was employed for the exchange-correlation functional. Our calculations were mainly performed on non-magnetic structures (that is, non-spin-polarized), but the effect of magnetization was also analysed with the results presented in Supplementary  Fig. 4. The unstable stacking-fault energy and the energy barrier for twinning were analysed with the nudged-elastic band method 48 implemented in the VASP package. To obtain the formation energy, the initially created lattice structure was subjected to geometrical optimization with high-precision calculations (the energy cutoff used in this work was 337.0 eV) on the G point of the Brillouin zone. Geometrical optimization was fully achieved when the total energy converged to within 10 À 4 eV between successive steps. Having optimized the volume while allowing the atoms to relax to their ground state, the formation energy (cohesive energy) was derived by subtracting the sum of single-atom energies from the total energy. Data availability. The data that support the findings of this study are available from the corresponding authors upon request.