Constructing material network representations for intelligent amorphous alloys design

Abstract

Designing high-performance amorphous alloys is demanding for various applications. But this process intensively relies on empirical laws and unlimited attempts. The high-cost and low-efficiency nature of the traditional strategies prevents effective sampling in the enormous material space. Here, we propose material networks to accelerate the discovery of binary and ternary amorphous alloys. The network topologies reveal hidden material candidates that were obscured by traditional tabular data representations. By scrutinizing the amorphous alloys synthesized in different years, we construct dynamical material networks to track the history of the alloy discovery. We find that some innovative materials designed in the past were encoded in the networks, demonstrating their predictive power in guiding new alloy design. These material networks show physical similarities with several real-world networks in our daily lives. Our findings pave a new way for intelligent materials design, especially for complex alloys.

Figures (5)

• Figure 1: Network representations and analyses for amorphous alloys. (a) Network of binary alloys. The nodes are different elements colored by their periodic groups. Their diameters are scaled based on the atomic radii. Each edge dictates an experimentally discovered amorphous alloy with the two nodes at a certain year (see color bar). There are 38 nodes and 94 edges. (b) The network of binary alloys by 3D printing. (c) Clique size distribution of the binary network. $\mathcal{N}_{\mathcal{S}}$ of $\mathcal{S}=1$ gives the number of nodes in (a). The light-shaded bars represent all possible geometric objects (${\bf C}_{38}^{\mathcal{S}}$) in the network, like rectangles for $\mathcal{S}=4$. (d) Network of ternary alloys. It is plotted in the same way as (a) but based on triangles. Each triangle represents a ternary system. There are 47 nodes and 352 triangles, generating 348 edges. (e) The network of ternary alloys by 3D printing. The color schemes in (d) and (e) are the same as (a) and (b), respectively. (f) Clique size distribution of the ternary network, similar to (c). The numbers for the light-shaded bars are ${\bf C}_{47}^{\mathcal{S}}$. (g) A periodic table highlighting elements used in (d). The color bar depicts the number of ternary alloys an element is involved in. The big letter "B" or "T" marks an element showing up in the binary or ternary network. (h) The numbers of edges and triangles of an element in the binary and ternary networks, normalized by the corresponding largest number. The largest degree in (a) is 16, and the largest number in (g) is 93.
• Figure 2: Discovery history of amorphous alloys. (a) A Sankey diagram illustrating the invention histories of binary ($B_n$) and ternary ($T_n$) amorphous alloys from 1960. They are classified based on how many elements have been used in the previously developed amorphous alloys. For example, $B_1$ of 1988 demonstrates that one of the elements was used in the binary alloys developed before 1988. (b) Topology evolution of dynamical networks. The upper panel shows the number of nodes $\mathcal{N}_{\rm node}$, while the lower panel exhibits the number of links ($\mathcal{A}_2$) and triangles ($\mathcal{A}_3$) for the binary and ternary network, respectively.
• Figure 3: Triangle analysis in the ternary network. (a) Schematic illustration of triangle classification. By adding new triangles ( CDE and ABX, marked by the dashed red lines), there are three types of triangles in addition to the existing ones. The blue triangle ( BCE) automatically forms (Auto). The red triangle ( ADE) lacks an edge so it is a fake triangle (Fake). The green triangle is created by adding a new node so it is unknown from the left (Unknown). (b) The yearly growth of the number of classified triangles $\mathcal{N}_\Delta$. The number of publications $\mathcal{N}_{\rm pub}$ from the shown queries from the Web of Science database are imposed as lines for comparison. (c) A Sankey plot explaining the source of the developed ternary alloys (Real) at each year from the three groups. (d) Triangle tracking by cross-comparing the binary and ternary networks. The outer shows the source of the 352 developed ternaries from the binary network (T2B). The inner illustrates the source of the 62 automatically formed triangles in the binary network from the ternary network (B2T).
• Figure 4: Scaling properties of the material networks. (a) Probability distribution of the network entity. We consider the degree of nodes ($k_2$) and the number of triangles of nodes ($k_3$) in the binary and ternary networks, respectively. They are captured by a pow-law relation, $P(k_n)\sim k_n^{-\gamma}$ with $\gamma \approx 1.5$ (the dashed line). (b) The dependence of the maximum of $k_n$ on the number of nodes $\mathcal{N}_{\rm node}$ from the dynamical networks (see Fig. \ref{['fig2']}). The dotted lines represent a power-law scaling, $k_{n}^{\rm max} \sim \mathcal{N}_{\rm node}^{1/(\gamma-1)}$, where $\gamma \approx 1.5$ for both. The orange dot-dashed line represents a logarithmic scaling for a random network ($k_{n}^{\rm max} \sim \ln \mathcal{N}_{\rm node}$).
• Figure 5: Scaling properties of the real-world networks. The probability distributions of these networks are fitted to the power-law decay behaviour. (a) The Chinese flight network. The subgroup data for China Eastern Airlines (MU), China Southern Airlines (CZ), and Air China (CA) are shown for comparison. (b) The US flight network. The subgroup data for Delta Airlines (DL), United Airlines (UA), and Southwest Airlines (WN) are shown for comparison. (c) The email communication network. (d) The blog network. The power-law scaling, $P(k_n)\sim k_n^{-\gamma}$, holds for all these cases with $\gamma \approx 1.5$ for (a) and (b), and $\gamma \approx 1.8$ for (c) and (d).