Lattice dynamics of ${\mathrm{Yb}}_x{\mathrm{Co}}_4{\mathrm{Sb}}_{12}$ skutterudite by machine-learning interatomic potentials: Effect of filler concentration and disorder

Lattice dynamics determines a number of important properties of solids. While computational methods with predictive power have been developed in this area, the task is still difficult for the complex compounds. We present a method for automatic on-the-fly generation of multicomponent interatomic potentials. The method is based on active learning, which ensures effective extrapolation to new atomic environments. The accuracy is then demonstrated on the example of the Yb-filled skutterudite compound ${\mathrm{Yb}}_x{\mathrm{Co}}_4{\mathrm{Sb}}_{12}$, which is a family of the promising thermoelectric materials. Atomic displacements, vibrational spectrum, and lattice thermal conductivity were obtained and the effect of the Yb filling and ordering was studied as 700 K. The potential allowed us to reproduce fine features of the vibrational spectrum, as well as the reduction of the lattice thermal conductivity with filling. We found only a small effect of the disorder on the vibrational spectrum and the thermal conductivity.

Figure 1

Computational cells of ${\mathrm{Yb}}_{0.125}{\mathrm{Co}}_4{\mathrm{Sb}}_{12}$ with periodic (left) and random (right) distributions of Yb fillers. Only Yb-filled icosahedra of ${\mathrm{Sb}}_{12}$ are shown.

Figure 2

Phonon density of states of ${\mathrm{Yb}}_x{\mathrm{Co}}_4{\mathrm{Sb}}_{12}$ for (left to right): $x=0.25$, 0.125, 0. Red and blue lines show the results of interatomic potential and DFT, correspondingly.

Figure 3

Distribution of atomic displacements (over MD trajectory) of each atom type in ${\mathrm{Yb}}_{0.296}{\mathrm{Co}}_4{\mathrm{Sb}}_{12}$ at 700 K. The distribution of the Yb atoms is random.

Figure 4

Vibrational density of states in ${\mathrm{Yb}}_{0.2}{\mathrm{Co}}_4{\mathrm{Sb}}_{12}$ at 700 K for the periodic (left) and random (right) distribution of the Yb atoms. The insets show the Yb spectrum separately. The filled area is the total density of states.

Figure 5

Calculated values of lattice thermal conductivity (open symbols) and experimental data [18, 42] (filled symbols) for ${\mathrm{Yb}}_x{\mathrm{Co}}_4{\mathrm{Sb}}_{12}$ at 700 K. Triangles and squares show periodic and random filler distribution, correspondingly. The vertical lines are the $95\%$ confidence interval of the mean, averaged over 20 trajectories. Several points at single concentration correspond to different random distributions of the Yb atoms.