Network analysis of synthesizable materials discovery

Abstract

Assessing the synthesizability of inorganic materials is a grand challenge for accelerating their discovery using computations. Synthesis of a material is a complex process that depends not only on its thermodynamic stability with respect to others, but also on factors from kinetics, to advances in synthesis techniques, to the availability of precursors. This complexity makes the development of a general theory or first-principles approach to synthesizability currently impractical. Here we show how an alternative pathway to predicting synthesizability emerges from the dynamics of the materials stability network: a scale-free network constructed by combining the convex free-energy surface of inorganic materials computed by high-throughput density functional theory and their experimental discovery timelines extracted from citations. The time-evolution of the underlying network properties allows us to use machine-learning to predict the likelihood that hypothetical, computer-generated materials will be amenable to successful experimental synthesis.

Fig. 1

Network representation of material phase diagrams. The schematic illustrates phase diagrams with the order of the system ranging from two-dimensional binary to the 89-dimensional materials stability network central to this work. The energy-composition convex-hull is shown for the binary system, and all higher-order phase diagrams are projections of their respective N-dimensional convex-hulls to two dimensions, where materials are represented as nodes and tie-lines as edges. For clarity, only those tie-lines connected to high-degree nodes are shown in the materials stability network, where the sizes of the nodes are also scaled to reflect their degree

Fig. 2

Evolution of the size of the materials stability network. a Time evolution of the number of stable materials (i.e., nodes), N, and tie-lines (i.e., edges), E, and (b) how the number of nodes and tie-lines vary with respect to each other. A tie-line is included in the evolving network only after both nodes it is connecting to are identified as discovered. Dashed lines in (a) are extrapolations of N and E from the available data (markers and solid lines) by fitted quadratic polynomials. Dashed line in (b) is a linear fit to the data (circles). Fits performed in both panels exclude the first four times steps to obtain fits that are more representative of more recent times. A plot of the number of stable materials discovered each year as a function of time is also available in Supplementary Fig. 1

Fig. 3

Degree distribution among stable materials discovered by the year 2010. The complementary cumulative distribution function (P(k)) of the degree distribution p(k) of stable materials (circles) is plotted along with the fitted distributions (solid lines). Each point P(k) represents the probability that a material has greater than k tie-lines connected to it in the network. Power-law, truncated power-law (with exponential cutoff), and positive log-normal distributions are labeled as PL, tPL, and pLN, respectively. The dashed line shows k_min, the lowest degree used in fitting. Degree distributions of other times are shown in Supplementary Fig. 1

Fig. 4

Network evolution and properties of the machine-learned synthesizability models. a Time evolution of the local environments of two sample materials (marked with open circles), superconductor YBa₂Cu₃O₆, and thermoelectric BiCuSeO, in the materials stability network. Materials (nodes) discovered by a given temporal state of the network are shown in blue, whereas those awaiting discovery are red. Node size is proportional to degree. b Time evolution of the network properties of sample materials YBa₂Cu₃O₆ and BiCuSeO, namely, degree and eigenvector centralities (C_k and C_e), degree (k), mean-shortest-path $\left(\ell \right)$, mean degree of neighbors (k_n), and clustering coefficient (C), where the vertical dashed lines show the approximate time of discovery. c Feature contributions to the RF model as derived from the Gini importance. d Pearson correlation coefficients of time-dependent network properties used in models as features, where pt and tt denote past time and target time, respectively, corresponding to a given sequence of window size of two (see “Methods”). Variables and names of network properties are used interchangeably in (b), (c), and (d)

Fig. 5

Extraction of sequences from temporal network property data using a sliding window to use as input for machine learning. The vector Y_i stores the targets to be learned for material i, i.e., encoding whether i is discovered by a given time-step t or not (as binary labels 1 and 0). C_i, k_i, and ${\ell }_i$ are examples for vectors of different network properties, encoding how those properties change over time as the network evolves, as explained in the text. The process of applying a sliding window (here with a width of w = 2) to extract sequences of features and targets (x_i,t, y_i,t) is illustrated. ML stands for the machine-learning task of training and testing classification algorithms using the extracted data