Guided Self-Assembly of Nano-Precipitates into Mesocrystals

We show by a combination of computer simulation and experimental characterization guided self-assembly of coherent nano-precipitates into a mesocrystal having a honeycomb structure in bulk materials. The structure consists of different orientation variants of a product phase precipitated out of the parent phase by heterogeneous nucleation on a hexagonal dislocation network. The predicted honeycomb mesocrystal has been confirmed by experimental observations in an Mg-Y-Nd alloy. The structure and lattice parameters of the mesocrystal and the size of the nano-precipitates are readily tuneable, offering ample opportunities to tailor its properties for a wide range of technological applications.

Scientific RepoRts | 5:16530 | DOI: 10.1038/srep16530 a plate shape with α {1100} habit plane. This triadic structure originates from the breaking of the three-fold symmetry of the hexagonal close-packed (h.c.p.) matrix during the α − Μ g to β 1 transformation. According to the lattice correspondence proposed for the α − Μ g (point group: 6/mmm) to β 1 (point group: m m 3 ) transformation 19 1 , there are three equivalent transformation pathways, leading to three crystallographically equivalent correspondence variants of the β 1 phase [18][19][20][21][22] . Each correspondence variant can generate two orientation variants by two opposite rigid-body rotations (clockwise or counter-clockwise) (Fig. 1). For example, the lattice of the correspondence variant ② can rotate clockwise or anticlockwise to form a plate with the (1-100) or (01-10) habit plane, leading to two orientation variants designated as variant ② + or ② − . For a given plate, stress concentration exists near its end rims, which becomes the dominant driving force for self-assembly. If three such plates belonging to different correspondence variants can form in a triadic assembly (i.e., ① + /② + /③ + or ① − /② − /③ − ), then the stress concentrated at one end rim of each plate can be largely removed. Such a triadic assembly has been observed in both experiments 19,[22][23][24]) and computer simulations [20][21] (Fig. 2b).
Such a stable triadic assembly provides the basic building block of an interconnected honeycomb structure (a hexagonal network of β 1 precipitates, Fig. 2c). However, even with autocatalysis caused by the long-range elastic interactions, nucleation of β 1 precipitates is a stochastic process and the triadic building blocks will not arrange themselves into a honeycomb structure without appropriate guidance. Thus, a template that not only lowers the activation energy barrier for β 1 nucleation at desirable sites, but also selects a proper β 1 variant for a given site (i.e., variant selection) is needed. We will show below that a hexagonal dislocation network consisting of three sets of screw dislocations (all right-handed or left-handed) is an ideal candidate template. This type of dislocation network is frequently observed on (0001) plane in h.c.p. crystals or on {111} planes in face-centred cubic (f.c.c.) crystals [24][25][26][27][28][29][30][31][32][33] , which is equivalent to a pure 〈 0001〉 or 〈 111〉 twisted grain boundary, respectively. To explore whether such a dislocation network can bias nucleation and guide the self-assembly of β 1 precipitates into a honeycomb structure, the interaction energies between the dislocation network and correspondence variants of β 1 phase are firstly calculated. The interaction energy between a pre-existing screw dislocation, i.e., a line segment of the hexagonal dislocation network, and a to-be-nucleated β 1 particle having a stress-free transformation strain (SFTS) of ε ij p is given by 34,35 : where σ ij dis is the stress field around the dislocation and  spacing of the slip plane [36][37][38][39][40][41][42][43][44] . The ε ij p is the SFTS of the p-th correspondence variant of β 1 (p = ① , ② and ③ ). A negative value of the interaction energy means that the formation of β 1 under the influence of the stress field of the dislocation is energetically favoured. It is found that, within the basal plane containing the dislocation network, the interaction energies for all β 1 variants are zero. For the plane lying one Burgers vector (a typical cut-off radius for dislocation core) above the segment of the dislocation network with = / α b a 3[1120] , the interaction energies for the correspondence variants ① , ② and ③ are 10.15, 0.0 and -10.15 KJ/mol, respectively. These results mean that only variant ③ is favoured. Via further examination of the two orientation variants ③ + and ③ − associated with the correspondence variant ③ , we find that only variant ③ − has its habit plane parallel to the pre-existing screw dislocation line and, thus, is the most favoured orientation variant. Similarly, for the plane lying below the dislocation-network-containing plane by one Burgers vector, the interaction energies for the three correspondence variants ① , ② and ③ are − 10.15, 0.0 and 10.15 KJ/mol, respectively. In this case, the orientation variant ① + becomes the most favoured one (Fig. 3a).
When a hexagonal screw dislocation network is introduced, the interaction energy calculation results suggest that the orientation variants ① − , ② − and ③ − (represented by different colours) will form preferably on one side of the dislocation network in an alternating sequence, Fig. 3b, the growth of which will eventually lead to a mesocrystal having a honeycomb structure. Similarly, a mesocrystal of a honeycomb structure consisting of alternating distributed variants ① + , ② + and ③ + will form on the other side of the dislocation network. The lattice parameter of the mesocrystal is determined by the size of the unit cell of the dislocation network that depends solely on the twist angle. The size of the mesocrystal is determined by the equilibrium volume fraction of the precipitate phase. According to Frank's formula 25,28 , the size of the unit cell (i.e., the hexagon) in a dislocation network increases as the  twist angle decreases. Thus, the maximum size of the hexagon is limited by the grain size of the α−Mg matrix, while the minimum size is dictated by the core width of the dislocation, which is determined by the interplay between the crystalline energy and the elastic strain energy 25,29 .
To examine whether such a dislocation-guided self-assembly of β 1 precipitates would lead to a mesocrystal of the honeycomb structure, heterogeneous nucleation and growth of β 1 precipitates are simulated by the phase field method. By introducing the stress field of a dislocation network, as described above, the nucleation of β 1 precipitates is simulated by using the Langevin random force term. In the simulations, the edge length of the hexagonal dislocation network is set to be 150 nm (corresponding to a misorientation angle of 0.01°), and the Burgers vector of each segment of the dislocation network is shown in Fig. 4a. In the early stages, isolated β 1 particles nucleate on the dislocation network and grow along the dislocation line segments, Fig. 4b. Note that the precipitates on different sides of the plane containing the dislocation network cannot grow across the plane because it is elastically unfavourable. When all these particles impinge upon each other, a honeycomb structure of alternating β 1 orientation variants forms, Fig. 4c. With prolonged ageing, the β 1 precipitates grow mainly along the [0001] α direction forming thin plates, until the equilibrium volume fraction of the β 1 phase is reached, Fig. 4d.
The experimental support to the above design and simulation prediction is shown in Fig. 5. Figure 5a shows a honeycomb network of β 1 plates in the WE54 alloy that has been solution treated for 8 hours at 525 °C (798 K), water quenched and aged for 10 hours at 250 °C (523 K). To facilitate the visualization, the sample was deeply etched to remove the α -Mg matrix inside each hexagon of the honeycomb structure. The hexagons in this honeycomb structure have edge length ranging from 150 to 300 nm. For each hexagon, each of its 6 faces is made by a single β 1 plate, as shown more clearly by the high-angle annular dark-field scanning transmission electron microscopy image, Fig. 5b.

Discussion
As a commonly observed physical phenomenon, symmetry breaking accompanying solid-state phase transformations provides a natural way to achieve self-accommodated domain structures. Depending on the final structure required, an appropriate phase transformation should be selected according to crystal symmetry and phase transformation mechanism. In our case, because three correspondence variants and three different habit planes are necessary to build the honeycomb structure, the h.c.p. to cubic phase transformation in the Mg-Y-Nd alloy system is selected. During the transformation, the (0001) α plane transforms into ( ) β 110 1 plane and thus the three-fold rotational symmetry of the h.c.p. structure is broken, leading to three crystallographically equivalent correspondence variants. Such a symmetry breaking generates the basic building block, i.e., the triadic assembly of three β 1 variants, which guarantees the stability of the building block. This is essential for a honeycomb mesocrystal. Because of undergoing different transformation pathways and having different SFTS, the three β 1 variants can respond distinctively to the stress fields of different dislocations, which governs the variant selection and self-assembly process. Such a selection originates from the correspondence between the dislocations and the β 1 variants (e.g., the dislocation with the Burgers vector / α a 3[1120] leads to variants ① + and ③ − ), both of which are dictated by the breaking of the three-fold symmetry of the h.c.p. lattice. Since the eigenstrains of both precipitates and dislocations are related directly to the crystal structure, a feasible design strategy based on the phase transformation crystallography to produce self-assembled mesocrystals with various structures and lattice parameters can be proposed.
Comparing with existing methods of making regularly distributed second phase particles on substrates, the following distinctions of the method presented in this work should be noted: • Both the lattice parameters and the structure of the mesocrystal can be tuned by adjusting dislocation type and spacing via controlling the type (e.g., tilt, twist, mixed) and misorientation of grain boundaries. • The method can produce stacks of 2D mesocrystals or directly 3D mesocrystals by the utilization of 3D dislocation networks as templates. The resultant mesocrystal is easily scalable via standard physical metallurgy processes such as thermomechanical treatments. For example, pure twist and pure tilt grain boundaries can be created easily by polygonization of a twisted or bent single crystal upon annealing. • The symmetry and motif of the mesocrystal could also be controlled by choosing appropriate phase transformations between different crystal structures in different alloy systems. • The multiple variants in the honeycomb mesocrystal are dominated by symmetry breaking and long range elastic interactions, which provides distinctive symmetry characteristics comparing to the existing methods that produce mono-variant mesocrystals such as single variant f.c.c. (111) islands on f.c.c. (111) substrate. • The interaction energy calculation results and phase field simulation results indicate that the nanoprecipitates can form on both sides of the dislocation network, offering one more degree of freedom as compared to nano-island formation on substrates. • Because the mesocrystal synthesized in this study is thermodynamically stable, the compositions of the precipitate and matrix phases are in a tie-line, there is no mixing or interdiffusion between the precipitates and matrix and thus the system developed could be applied at relatively high temperatures up to the solvus temperature. • Since bulk samples are producible in this approach, one could explore mechanical properties in addition to the physical properties of these mesocrystals, which is rather difficult to do if using a thin film sample.
In summary, a new approach to develop mesocrystals is demonstrated through a combination of crystallographic design and defect engineering. The design concept and predicted mesocrystals have been confirmed by both computer simulation and experimental characterization. In the crystallographic design, symmetry breaking caused by a phase transformation is utilized, which provides a natural way to obtain fundamental building blocks for the mesocrytal. Furthermore, a hexagonal dislocation network is introduced to guide the self-assembly (via nucleation and growth) process of the precipitates leading to a honeycomb structure. Such a design method could provide a great deal of flexibility in synthesizing highly regular, highly tuneable nanostructures in bulk quantity, through crystallographic design of phase transformation and defect engineering of dislocations, and it is likely that many interesting mesocrystals could be produced. They were grit blasted and pickled in 15% nitric acid before delivery. Small blocks with a dimension of 10 × 5 × 20 mm were cut from one plate and re-solution treated for 8 hours at 525 °C, water quenched and aged for 10 hours at 250 °C. The alloy with nominal composition of Mg-3 wt% Nd was cast from high purity Mg and Nd by induction melting in a steel mould crucible under a protected argon atmosphere at 760 °C, and pouring into a preheated mould coated by graphite. Bulk samples with dimensions of 8 mm × 11 mm × 20 mm were covered by MgO powder, solution treated at 520 °C for 24 hours, followed by water quenching and ageing for 10 hours at 250 °C.

Methods
Scanning electron microscopy (SEM) and scanning transmission electron microscopy (STEM). The SEM samples were prepared from heat treated blocks, which were first ground on SiC sand papers with increasing fineness grades up to 2400-grit and subsequently polished by 1 μ m OPS suspension on Struers cloth. The samples were etched for about 10 seconds with a solution containing 29 ml picric acid, 41 ml water, 50 ml acetic acid and 350 ml ethanol. Secondary electron SEM images were recorded by a JSM-7001 F SEM with field emission gun working at 10 kV with a working distance of 15 mm and a probe current of 10 (~500 pA). For the preparation of TEM samples, small discs with a diameter of 3 mm were punched from strips cut from the heat treated blocks and manually ground to thicknesses around 150 μ m. The final TEM foils were prepared by twin-jet electro-polishing at − 55 °C and 0.1 A with a solution of 5.3 g lithium chloride, 11.16 g magnesium perchlorate, 500 ml methanol and 100 ml 2-butoxy-ethanol. The high-angle annular dark-field (HAADF) STEM images were acquired using a FEI Titan 3 80-300 operated at 300 kV, fitted with two CEOS aberration correctors, and a Fischione HAADF detector. In order to improve interpretability, the convergence angle was set to conservative 15.0 mrad, leading to a diffraction limited (Gaussian) probe diameter of ~0.12 nm.
Phase field simulation. In the model system, face centred cubic β 1 particles are precipitated out from the hexagonal α−Mg matrix under the influence of the stress field of a (0001) α twist grain boundary. Model inputs, including lattice parameters, precipitate-matrix orientation relationship, elastic constants and free energy data, are obtained from experimental characterization, ab initio calculations and thermodynamic databases.

Equipment and settings. The schematic diagrams in Figs. 1 and 2c were plotted by CorelDRAW
Home & Student X7. Figures 2b,3 and 4b,c,d were obtained according to phase field method and plotted by ParaView 3.8.0. The SEM image in Fig. 5a was processed using Image J 1.49B. The HAADF-STEM images in Figs. 2a and 5b were acquired using TEM image and analysis (TIA) software running in Titan. All the figures were combined and processed in CorelDRAW Home & Student X7.