Calculation of ionic conductivity at 300 K of Li₃OCl_1-xBr_x with M3GNet, a general force field based on graph neural networks#

On Advance/NanoLabo, an integrated GUI for nanomaterials, you can execute molecular dynamics simulation¹ with M3GNet², a general force field based on graph neural networks.

We introduce calculation of composition dependence of ionic conductivity at 300 K of a lithium superionic conductor $\text{Li}_3\text{OCl}_{1-x}\text{Br}_x$ via molecular dynamics simulation with M3GNet.

M3GNet, a general force field based on graph neural networks#

M3GNet is a universal interatomic potential based on graph neural networks with three-body interactions which was trained on the enormous data of structural relaxation recorded in Materials Project³.

Structural relaxation in Materials Project was executed via DFT calculation. M3GNet was trained on MPF.2021.2.8, a dataset which contains 62,783 compounds with 187,687 energies, 16,875,138 force components and 1,689,183 stress components.

M3GNet will enable you to execute molecular dynamics simulation with low computational cost, good accuracy and no need to parametrize force fields for each compound.

Li₃OCl_1-xBr_x, a lithium superionic conductor#

$\text{Li}_3\text{OCl}_{1-x}\text{Br}_x$ is a solid lithium superionic conductor. It is reported⁵ that ab initio molecular dynamics found $\text{Li}_3\text{OCl}_{0.75}\text{Br}_{0.25}(x=0.25)$ ⁴ is the highest conductivity $(\sim4×10^{-2} \text{ mS/cm}(\text{at 300 K}))$ composition.

We calculated composition dependence of ionic conductivity of $\text{Li}_3\text{OCl}_{1-x}\text{Br}_x$ via molecular dynamics simulation with M3GNet.

Generation of calculation models#

Firstly, we generated $2×2×2$ supercell models from the unit cell model of $\text{Li}_3\text{OCl}$ $(x=0)$ (mp-985585) downloaded from Materials Project

Secondly, we replaced $\text{Cl}$ with $\text{Br}$ to construct models corresponding to $x=0.25,0.5,0.75$ and $1$ , respectively. We adopted structures with highest symmetry for $x=0.25,0.5$ and $0.75$ , respectively⁶.

Finally, we introduced single $\text{Li}$ vacancy for each model by removing a $\text{Li}$ atom⁵.

Advance/NanoLabo enables you to generate such models on GUI easily.


Li₃OCl	Li₃OCl_0.75Br_0.25	Li₃OCl_0.5Br_0.5

Li₃OCl_0.25Br_0.75	Li₃OBr

Setting of calculation schemes#

We used M3GNet as force filed for all simulations.

First, we performed structural optimization under $0 \text{ bar}$ allowing cell to change anisotropically for each model. Simulation time step was $1 \text{ fs}$ .

Next, we heated each system up to the desired temperature $(900 ,1200 ,1500 ,1800 ,2100 \text{ K})$ at rate of $20 \text{ K/ps}$ and preformed isothermal molecular dynamics simulation for $5000$ steps ( $10 \text{ ps}$ ).

And finally, we calculated MSD (Mean Square Displacement) of systems at each temperature for $150000$ steps ( $300 \text{ ps}$ ).

We employed NVT ensemble as statistical ensemble for these dynamics calculation. We set simulation time step as $2 \text{ fs}$ .

On Advance/NanoLabo, you can calculate and visualize MSDs of each element just by turning on Diffusion Coefficient button.

Visualization of MSDs on GUI

Analysis results#

In a three-dimensional system, diffusion coefficient $D$ and MSD are related as $MSD = 6Dt$

where $t$ is simulation time. We calculated diffusion coefficient $D$ of $\text{Li}$ for each temperature by fitting the relationship to time dependence of MSD. We show Arrhenius plot of diffusion coefficient $D$ of $\text{Li}$ obtained for each system below.

Arrhenius plot of diffusion coefficient D

Ionic conductivity $\sigma$ is calculated from diffusion coefficient $D$ and temperature $T$ as $\sigma = \frac{\rho{e^2}}{kT}D$ $D = D_0\text{exp}\left(-\frac{\Delta E_a}{kT}\right)$

where $\rho$ is number density of $\text{Li}$ ion, $e$ is elementary charge, $k$ is Boltzmann constant and $\Delta E_a$ is activation energy.

We calculated activation energy $\Delta E_a$ and the constant $D_0$ for each composition by fitting the latter relationship to the Arrhenius plot. Then, we calculated composition dependence of ionic conductivity $300 \text{ K}$ from the obtained $\Delta E_a$ and $D_0$ . We show the result below.

We can see from the result that ionic conductivity increases to maximum value with increasing $x$ from 0 to 0.25, and monotonically decreases to minimum value with decreasing $x$ from 0.25 to 1 similarly to the result of ab initio molecular dynamics reported by previous study⁵. However, we note that the ionic conductivities of $\text{Li}_3\text{OCl}_{1-x}\text{Br}_x$ were underestimated compared to the result of ab initio molecular dynamics. The underestimation might have been caused by instability of M3GNet at high temperature leading overestimation of diffusion coefficient.

Composition dependence of ionic conductivity of Li₃OCl_1-xBr_x

Calculation of diffusion coefficient of a system at a certain temperature was done for about 2 hours without parallelization. It shows that molecular dynamics simulation with M3GNet has significantly low computational cost compared to ab initio molecular dynamics. Nevertheless, molecular dynamics simulation with M3GNet reproduced the tendency of composition dependence of ionic conductivity calculated via ab initio molecular dynamics.

Calculation of ionic conductivity at 300 K of Li3OCl1-xBrx with M3GNet, a general force field based on graph neural networks#