Ab initio Nonequilibrium Molecular Dynamics in the Solid Superionic Conductor ${\mathrm{LiBH}}_4$

The color-diffusion algorithm is applied to ab initio molecular dynamics simulation of hexagonal ${\mathrm{LiBH}}_4$ to determine the lithium diffusion coefficient and diffusion mechanisms. Even in the best solid lithium ion conductors, the time scale of ion diffusion is too long to be readily accessible by ab initio molecular dynamics at a reasonable computational cost. In our nonequilibrium method, rare events are accelerated by the application of an artificial external field acting on the mobile species; the system response to this perturbation is accurately described in the framework of linear response theory and is directly related to the diffusion coefficient, thus resulting in a controllable approximation. The calculated lithium ionic conductivity of ${\mathrm{LiBH}}_4$ closely matches published measurements, and the diffusion mechanism can be elucidated directly from the generated trajectory.

Figure 1

A snapshot of the model after equilibration at 535 K using the Gaussian isokinetic thermostat. Light and dark spheres: lithium atoms with $+1$ and $-1$ color charge, respectively.

Figure 2

The time-averaged response versus the external field strength (circles) from Table ; the black lines are guides for the eye.

Figure 3

The time integrated dissipative flux versus simulation time with the external field $F_e=0.05\mathrm{eV}{\AA }^{-1}$ in the (110) and (001) directions. A straight line without intercept is fitted to the steady state (from 3.5 ps onwards) to obtain the steady-state average flux $⟨J_c(t)⟩$.

Figure 4

The hopping sequence of two lithium atoms (labeled 1 and 2) observed in an NEMD trajectory [field along (110)]; only lithium atoms are shown as light and dark spheres. Lithium atoms jump into an empty hexagonal site (situated on the origins of the primitive cells) and from there jump into a free lattice site.