Elastic properties of bulk and low-dimensional materials using van der Waals density functional

In this work we present a high-throughput first-principles study of elastic properties of bulk and monolayer materials mainly using the vdW-DF-optB88 functional. We discuss the trends on the elastic response with respect to changes in dimensionality. We identify a relation between exfoliation energy and elastic constants for layered materials that can help to guide the search for vdW bonding in materials. We also predicted a few novel materials with auxetic behavior. The uncertainty in structural and elastic properties due to the inclusion of vdW interactions is discussed. We investigated 11 067 bulk and 257 monolayer materials. Lastly, we found that the trends in elastic constants for bulk and their monolayer counterparts can be very different. All the computational results are made publicly available at easy-to-use websites: https://www.ctcms.nist.gov/∼knc6/JVASP.html and https://jarvis.nist.gov/. Our dataset can be used to identify stiff and flexible materials for industrial applications.

Figure 1

Figure showing different classes of materials. Examples for (a) 3D-bulk diamond Si, (b) 2D-bulk 2H-${\mathrm{MoS}}_2$, (c) 1D-bulk ${\mathrm{MoBr}}_3$, (d) 0D-bulk ${\mathrm{BiI}}_3$ and (e) 2D-1L (${\mathrm{MoS}}_2$ monolayer) are shown. Dimensionality is reduced due to the presence of vdW bonding in one, two, or three crystallographic dimensions.

Figure 2

(a) Crystal system and (b) dimensionality distribution for materials in our database.

Figure 3

Comparison of Voigt (a) bulk and (b) shear modulus obtained from JARVIS-DFT(JV) OPT and Materials Project (MP) PBE data. The red dots are moduli for predicted low-dimensional bulk materials, while green dots are for the remaining materials, i.e., the non-vdW-bonded materials. Pearson coefficient close to unity suggests excellent agreement in the two datasets.

Figure 4

Periodic table trend for high bulk modulus material constituents. The bulk moduli of all the materials were projected on individual elements and their average contribution is shown. The colorbar is in the unit of GPa. A similar trend was found for shear modulus.

Figure 5

Correlation of the number of filled $d$ orbitals with the bulk modulus obtained by averaging the element projected bulk modulus for transition metals (shown in Fig. 4) over each periodic table column (ex: averaging the element projected bulk modulus among Ti, Zr, and Hf for $d=2$, where $d=\mathrm{filled}d\mathrm{orbitals}$). With the exception of W group, the trend is very clear and is in agreement with the observed behavior of a particular group of materials (carbides, nitrides, etc.).

Figure 6

Correlation of electronic and magnetic properties (band gap and magnetic moment) with bulk modulus.

Figure 7

Elastic constant distribution for 3D (magenta), 2D (green), 1D (blue), and 0D (red) materials.

Figure 8

Effect of dimensionality on ductile-brittle and Poisson ratio predictions. Scatter plot boundary regions for Pugh-Pettifor criteria predicting brittle and ductile nature of materials is shown in (a), while Poisson ratio distribution for 3D, 2D, 1D, and 0D materials is shown in (b) with magenta, green, blue, and red color lines, respectively.

Figure 9

Relation of exfoliation energy with anisotropic elastic constants of bulk layered materials.

Figure 10

Elastic constant distributions ($C_{11}$ and $C_{12}$) for monolayer (1L) materials.