Biphasic-modulated dewetting design
In this work, we realized diverse HEA polyhedra through a biphasic-modulated dewetting process. As illustrated in Fig. 1a, liquid metal covered with metal salts is utilized as the precursor film, where every element presented a uniform distribution (Supplementary Fig. 1). Then driven by the minimization of total Gibbs free energy of the metal film-substrate system, the metastable film would spontaneously dewet during the heating process15. Scanning electron microscopy (SEM) characterization indicated the film gradually dewetted into irregularly island-shaped particles due to Rayleigh-Plateau-like instability (Supplementary Fig. 2). Based on the principle of minimizing surface energy, the particle would undergo morphology restructuring toward energetically favorable configurations through mass migration and surface atomic rearrangement. Owing to the surface energy anisotropy of the crystal, the product finally would develop into Wulff polyhedral morphology through the self-confinement growth of crystals under near-equilibrium conditions (Fig. 1a). Meanwhile, along with the reaction process, different metal elements were alloyed into the particle. As shown in Fig. 1b, different from the sphere product through kinetics trapping techniques2, 7–9, the HEA polyhedra could be synthesized by our biphasic-modulated dewetting process with thermodynamic-dominant reaction characteristics. Moreover, from a thermodynamic point of view, surface energy could also play an important role in the formation of crystal faces. Figure 1c shows the surface energy of multiple metal elements (Supplementary Table 1). Liquid metals (Ga, Sn) possess smaller surface energy than other common transition metal elements, indicating they are beneficial to the realization of HEA polyhedra by decreasing the surface energy as a “metallic surfactant”.
Synthesis and characterizations of HEA polyhedra
As a result, the HEA polyhedra in a large area were shown in Fig. 2a, confirmed by SEM characterization. To investigate the crystal structure and the exposed crystal face of the HEA polyhedra, X-ray diffraction (XRD) and transmission electron microscopy (TEM) analyses were conducted. The corresponding XRD profile was shown in Supplementary Fig. 3. It matched the standard XRD pattern, belonging to the Pm–3m space group with cubic symmetry. According to the SEM (Fig. 2a) and TEM images (Fig. 2b), and the crystal structure, an ideal construction of the HEA polyhedron was sketched using Wulffmaker software that could display the particle shapes of the minimum free energy19. As shown in Fig. 2c, the ideal HEA polyhedron is a rhombicuboctahedron surrounded by 8 triangular {111} facets, 6 rectangular {100} facets, and 12 rectangular {110} facets, where every two adjacent facets possess an angle of 135°. The high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image of an individual HEA polyhedron was exhibited in Fig. 2b (left). The approximate regular octagon was consistent with the view from the [100] directions of the constructed model. The right of Fig. 2b showed the TEM image of the particle. Each apex angle was measured to be 135° approximately, consistent with the theoretical values from the geometric model as well. The atomic-resolution HAADF-STEM images showed the arrangement of atoms on the exposed planes, which featured (001), (011), and (1 − 11) planes with crystal spacings of 0.297, 0.212, and 0.171 nm, respectively (Fig. 2d). The interplanar crystal spacings also corresponded to XRD data. Besides, the corresponding energy dispersive X-ray spectroscopy (EDS) mapping indicated a uniform distribution of constituent elements in the polyhedral particle (Fig. 2e), demonstrating the formation of high entropy state without elemental separation.
Given that our strategy for the HEA polyhedra synthesis is based on the self-confinement growth of crystals under near-equilibrium conditions, the synthesis of diverse HEA polyhedra would be realized (Fig. 3). The quinary (GaPtFeCoNi) HEA polyhedra in a large area were observed on the substrate (Fig. 3a, left), where individual particles were shown in the middle panel of Fig. 3a to display shape in detail. XRD data indicated these particles took on the cubic structure (Supplementary Fig. 4). Combining the obtained morphology with crystal structure, the exposed facets can be indexed by Wulffmaker software. The deduced model with crystal plane marked matched with the real morphology of the product, featuring the polyhedral configuration enclosed with {111}, {100}, and {110} facets (Fig. 3a, middle). This has been demonstrated in the morphology images from different angles of view. According to the model, the corresponding surface area percentages of {110}, {100}, and {111} facets are 55.60%, 25.20%, and 19.20%, respectively (the pie chart of Fig. 3a). In general, the intrinsic surface energy would be lower if the crystallographic plane is more closely packed20. The largest area percentage of {110} facet is related to its property of the closest packing in the body-centred cubic (BCC) structure. EDS mapping confirmed all constituent metal atoms retained the homogeneous mixing state (Fig. 3a, right). Moreover, the HEA polyhedra with different appearances have also been generated in the same HEA system (GaPtFeCoNiCu). Different from the rhombicuboctahedron shape in Fig. 2, the GaPtFeCoNiCu HEA exhibited the polyhedral shape surrounded by {111}, {100} {110}, {211} and {311} planes, verified by the SEM images and geometrical model (Fig. 3b, left and middle). The particle also possessed a uniform elemental distribution (Fig. 3b, right). The EDS analysis revealed the elemental contents were different in the two kinds of HEA polyhedra (Supplementary Tables S2 and S3), indicating the crystal morphology could be modulated by the chemical compositions of HEAs. And the high-index facets (i.e. {211} and {311}) with high surface energy appeared in the morphology of Fig. 3b, demonstrating liquid metal is beneficial to stabilize the shape with high-index facets. In addition to the cubic crystal system, the strategy can also be extended to the synthesis of HEA polyhedra with a hexagonal structure. As shown in Fig. 3c, the SnPtCoNiCu alloy exhibited a spindle-like shape. The SEM images and geometrical model indicated the {001}, {111}, and {110} crystal faces were exposed. The XRD measurement showed the formation of a hexagonal crystal structure, belonging to the P63/mmc space group with hexagonal symmetry (Supplementary Fig. 5). The atomic-resolution HAADF-STEM image of SnPtCoNiCu along the [001] zone axis matched with the XRD pattern (Supplementary Fig. 6). Combined with the uniform elemental distribution in the right of Fig. 3c, the polyhedral sample can be regarded as a high-entropy solid solution with a hexagonal structure. These results demonstrated the feasibility of our strategy for diverse polyhedral shapes, chemical compositions, and crystal structures of HEAs.
Mechanism investigation
To investigate the modulation of liquid-solid biphase in dewetting process, we deposited different metal films (Pt and Au) on the substrate as the precursor. Meanwhile, the synthesis without liquid metal or other metal films was carried out for comparison. It has been reported that sufficient atomic diffusion could enable atoms to arrive at their final destinations so that the Gibbs free energy of the entire system can reach a minimum value12,21. According to the Arrhenius-type equation, there is a negative correlation between diffusion activation energy and diffusion rate. Owing to the larger activation energy of the solid phase than that of the liquid phase22, the liquid would exhibit a larger diffusion rate, which led to unique growth kinetics of various materials23,24. Therefore, integrating liquid metal with the dewetting process is beneficial to regulate the surface restructuring behavior. When the dewetting and alloying process occurred, the solid film of the precursor was away from the liquid state at the reaction temperature owing to the high melting points of Au, Pt, and other metal elements. The surface diffusion of metal elements is relatively slower than that of the process participated with liquid metal, which made regular polyhedral shape harder to obtain under the same reaction condition. All samples showed an irregular morphology (Supplementary Figs. 7 to 9). Besides, the elemental mappings of the sample were conducted in the HAADF-STEM mode. Uniform elemental distribution was observed for PtFeCoNiCu alloy systems with Pt film or only metal salts as the precursor (Supplementary Figs. 7b and 9b). However, the AuPtFeCoNiCu system suffered from severe phase separation (Supplementary Fig. 8b), which originated from the immiscibility among elements and was similar to the previous study25,26. Compared with the PtFeCoNiCu and AuPtFeCoNiCu products, the shape of HEA polyhedra synthesized with the assistance of liquid metal (i.e., Ga and Sn film in Figs. 2 and 3) was closer to the regular shape, which verified the liquid fluidity could prompt atom rearrangement and morphology reconfiguration.
To further explore the formation mechanism of HEA polyhedra, the surface energy of Ga-containing and Ga-free HEAs was calculated by density functional theory (DFT) calculations (Fig. 4a). In the presence of Ga, the surface energies of different crystal faces in the GaPtFeCoNiCu HEA system of Fig. 2 are significantly decreased compared to that of Ga-free system, signifying a higher energetically stability. Specifically, the surface energies of the former and the latter are 2.447 J/m2 and 4.523 J/m2 on (100), 2.537 J/m2 and 5.067 J/m2 on (111), 2.330 J/m2 and 4.763 J/m2 on (110) crystal faces, respectively (Supplementary Table 4). The theoretical crystal shape was obtained by Wulffmaker based on the calculated surface energy19. The results are close to experiments (Fig. 4b). Additionally, the surface energies of HEA polyhedra containing high-index facets such as (211) and (311) have also been calculated (Supplementary Table 5). Notably, besides three low-index surfaces, the high-index surface energy in the Ga-containing system is also lower (Supplementary Fig. 10a), further demonstrating Ga could effectively reduce the surface energy. The deduced model was shown in Supplementary Fig. 10b, exhibiting a relatively consistent shape with experiments. Moreover, Monte Carlo (MC) combined with time-stamped force-bias Monte Carlo (tf-MC) simulations27,28 was conducted to investigate the evolution process from the perspective of kinetics (Fig. 4c, Supplementary Figs. 11 to 13). The dynamics simulation confirmed that GaPtFeCoNiCu HEA exhibited a BCC structure at 1000 K, consistent with the XRD result (Supplementary Figs. 3 and 12). Owing to the high computational complexity of HEA systems, we then carried out the simulation of the kinetic formation process at 300 K. The initial atomic models of Ga-containing and Ga-free HEA systems were spheres cut from the corresponding bulk model with BCC structure, exhibiting a morphology similar to polyhedron due to the relatively small number of atoms. After MC/tf-MC simulation with 5 ns, compared with the obvious irregular appearance of the Ga-free system, the polyhedral shape was still maintained in the GaPtFeCoNiCu (Fig. 4c). Different from the amorphous state in the Ga-free system, GaPtFeCoNiCu system could remain crystalline (Supplementary Fig. 13), which could lead to the different morphology evolution process. The energy-time curve revealed the simulation decreased system energy, indicating the morphology transformation is energetically favorable. As a consequence, the developed polyhedron of GaPtFeCoNiCu is relatively stable. Meanwhile, the energy fluctuation of GaPtFeCoNiCu was lower than that of the Ga-free system after the two systems reached the equilibrium state (Fig. 4c), indicating the presence of Ga with low surface energy contributed to better stabilize the system by decreasing the system energy. Finally, to demonstrate the utility of HEA polyhedra, we studied the electrocatalytic activities toward alkaline hydrogen evolution reaction (HER). As shown in Supplementary Fig. 14, the overpotential at the current density of 10 mA cm− 2 (η10) and the Tafel slope of HEA polyhedra was 36 mV and 44 mV dec− 1, respectively, demonstrating the sample was catalytically more active than HEA nanoparticles (η10 = 40 mV, Tafel slope = 57 mV dec− 1) and commercial Pt/C catalysts (η10 = 49 mV, Tafel slope = 68 mV dec− 1).