Predicting phase preferences of two-dimensional transition metal dichalcogenides using machine learning

Two-dimensional transition metal dichalcogenides (TMDs) can adopt one of several possible structures, with the most common being the trigonal prismatic and octahedral symmetry phases. Since the structure determines the electronic properties, being able to predict phase preferences of TMDs from just the knowledge of the constituent atoms is highly desired, but has remained a long-standing problem. In this study, we applied high-throughput quantum mechanical computations with machine learning algorithms to solve this old problem. Our analysis provides insights into determining physiochemical factors that dictate the phase preference of a TMD, identifying and going beyond the attributes considered by earlier researchers in predicting crystal structures. A knowledge of these underlying physiochemical factors not only helps us to rationalize, but also to accurately predict structural preferences. We show that machine learning algorithms are powerful tools that can be used not only to find new materials with targeted properties, but also to find connections between elemental attributes and the target property/properties that were not previously obvious.

Figure 1

Schematic representation of (a) 1H and (b) 1T phase, traditional and Janus TMD monolayers. The Janus structure consists of two different chalcogens ($X$ and $Y$) on two faces of a TMD. (c) Periodic table highlighting the transition elements and the chalcogen atoms considered for the combinatorial study. (d) Flow chart of systematic combinatorial search of traditional and Janus monolayers. (e) Pie charts showing the % distributions of the most stable magnetic orderings—ferromagnetic (FM), antiferromagnetic (AFM), and nonmagnetic (NM)—for 1H phase and 1T phase TMDs.

Figure 2

Heatmaps showing calculated formation energies (in eV per formula unit) of traditional and Janus TMD monolayers of (a) $3d$-, (b) $4d$-, and (c) $5d$-series elements in their most stable phase. The values printed in black (red) color correspond to the TMDs that prefer the 1H phase (1T phase). Black boxes highlight examples of TMDs that have already been synthesized in either the 1H phase or 1T phase, whereas those in pink already exist in multilayers or in bulk, with a possibility of creating monolayers from those structures.

Figure 3

Down-selection of features: Pearson correlation for (a) all thirteen features from Set B and (b) seven down-selected features from Set B, summarizing the pairwise correlation of different features among themselves and with the target property vector (formation energy $\mathrm{\Delta }{E}_f$). The target property and the features are listed along the diagonal; the blue and red color correspond to positive and negative correlation coefficients, respectively. The boxes in the lower triangle and the pie charts in the upper triangle are two different pictorial representations of the same information, with the absolute value of the associated Pearson correlation coefficient given by either the lighter and darker shades of the colors in the boxes, or the filled fraction of the pie chart. (c) Relative importance of Set B feature vectors in predicting the formation energies of TMDs computed using the RF algorithm. The subscript $\overline{\text{X}}\mathrm{M}$ indicates that the down-selected compound features are obtained as differences of the average of attributes of the chalcogens with the that of the metal atom's attributes.

Figure 4

Formation energy vs the down-selected feature vectors for different TMDs in: [(a)–(f)] the 1H phase and [(g)–(l)] 1T phase. Along the $x$ axis, the compound feature vectors are computed from elemental features according to ${\mathcal{F}}_{\overline{\text{X}}\text{M}}=\frac{1}{2}({\mathcal{F}}_{\text{X}}+{\mathcal{F}}_{\text{Y}})-{\mathcal{F}}_{\text{M}}$.

Figure 5

Parity plots of formation energies of: (a) 1H, (b) 1T phases of TMD monolayers, and (c) the entire dataset. The DFT computed formation energies are along the abscissa and those predicted using RF along the ordinate. Each dataset is divided such that 90% of the data is used to train the RF regression model and 10% data is used for validation of the model. The error bars on each data point correspond to prediction errors.

Figure 6

Phase-preference prediction performance of RF classification algorithm for the 180 down selected TMDs (see Fig. 2). The boxes marked with an $“{\mathrm{X}}^{\prime \prime }$ correspond to systems that were not predicted accurately by our model. We consider our prediction to be accurate if we obtain the correct phase at least 90% of the time.