Computational study of ${\mathrm{Li}}_3{\mathrm{BO}}_3$ and ${\mathrm{Li}}_3{\mathrm{BN}}_2$ I: Electrolyte properties of pure and doped crystals

Both ${\mathrm{Li}}_3{\mathrm{BO}}_3$ and ${\mathrm{Li}}_3{\mathrm{BN}}_2$ materials have promising properties for use in all-solid-state batteries and other technologies dependent on electrolytes with significant ionic conductivity. As the first of a two-part study, this paper reports the analysis of detailed simulations of Li ion diffusion in the monoclinic forms of these materials. Using both NEB and MD methods, it is clear that Li ion migration via vacancy mechanisms provides the most efficient ion transport in each material. While the results suggest that interstitial defects in these materials do not play a direct role in Li ion migration, their relative stability seems to enhance vacancy production via the formation of Frenkel-type defects. This may partially explain why the Li ion conductivities computed from MD simulations of samples initially containing a single Li ion vacancy are in reasonable agreement with measured values of this work for ${\mathrm{Li}}_3{\mathrm{BO}}_3$ and those reported in the literature for poorly crystalline samples of both materials. The possibility of increasing vacancy concentrations by substitutional doping (F for O in ${\mathrm{Li}}_3{\mathrm{BO}}_3$ and C for B in ${\mathrm{Li}}_3{\mathrm{BN}}_2$) is also examined, finding simulated conductivities comparable to those of the ideal vacancy model.

Figure 1

Ball and stick diagram of ${\mathrm{Li}}_3{\mathrm{BO}}_3$ with Li, B, and O represented by three shades of blue, black, and red balls, respectively. Dark, medium, and light blue shades correspond to $\mathrm{Li}\left(1\right)$, $\mathrm{Li}\left(2\right)$, and $\mathrm{Li}\left(3\right)$ types, respectively. Equivalent I-int sites are shown with green balls.

Figure 2

Ball and stick diagram of ${\mathrm{Li}}_3{\mathrm{BO}}_3$ with Li, B, and N represented by three shades of blue, black, and gray balls, respectively. Dark, medium, and light blue shades correspond to $\mathrm{Li}\left(1\right)$, $\mathrm{Li}\left(2\right)$, and $\mathrm{Li}\left(3\right)$ types, respectively. Equivalent I-int sites are shown with green balls.

Figure 3

(a) Ball and stick diagram for vacancy migration in ${\mathrm{Li}}_3{\mathrm{BO}}_3$ with Li, B, O, and F represented by three shades of blue, black, red, and pink balls, respectively. Labels indicate vacancy sites for migration pathway. (b) Configuration energy diagram results of NEB calculation of Li ion vacancy migration along the indicated pathway. The energies for these diagrams are adjusted for the lowest energy of the considered configurations, consistent with Table 1.

Figure 4

(a) Ball and stick diagram for vacancy migration in ${\mathrm{Li}}_3{\mathrm{BN}}_2$ with Li, B, C, and N ions represented by three shades of blue, black, brown, and gray balls, respectively. Labels indicate vacancy sites for migration pathways. The configuration energy diagrams from NEB calculations for Li ion vacancy migrations along the $\mathbf{a}$ axis and within $\mathbf{bc}$ plane are shown in (b) and (c), respectively. The energies for these diagrams are adjusted for the lowest energy of the considered configurations, different for the I-vac and C-doped models and consistent with Table 2.

Figure 5

Configuration energy diagram for the kick-out mechanism in ${\mathrm{Li}}_3{\mathrm{BN}}_2$ together with an inset diagram of the involved sites. In the diagram, Li ions at host sites are represented using the same convention as in Fig. 4 while interstitial sites are represented with green balls.

Figure 6

Plots of $\mathrm{MSD}(t,\langle T\rangle )$ from Eq. (10) in units of ${\AA }^2$ as a function of time in units of picoseconds for the stoichiometric, I-vac, and F-doped models of ${\mathrm{Li}}_3{\mathrm{BO}}_3$ at average temperatures of $\langle T\rangle =968$, 998, and 996 K, respectively.

Figure 7

Ball and stick diagrams of MD simulations for (a) I-vac ${\mathrm{Li}}_3{\mathrm{BO}}_3$ at temperature $\langle T\rangle =996\mathrm{K}$ and (b) F-doped ${\mathrm{Li}}_3{\mathrm{BO}}_3$ at temperature $\langle T\rangle =998\mathrm{K}$. B, O, and F are shown at their initial positions with black red, and pink balls, respectively. Li positions of the initial configuration and 290 subsequent positions at time intervals of 0.24 ps are indicated with gray balls. Simulations were performed using microcanonical NVE ensembles in $3\times 1\times 1$ supercells. The diagram represents a projection onto the $\mathbf{b}\mathbf{c}$ plane.

Figure 8

Plot of computational and experimentally measured values of ${log}_{10}\left(\sigma T\right)$ versus $1000/T$ for the I-vac and the F-doped models of ${\mathrm{Li}}_3{\mathrm{BO}}_3$. The computed values of $\sigma$ were determined from Eq. (13). Lines represent least squares fits to the ${log}_{10}\left(\sigma T\right)$ data. The experimental results for polycrystalline ${\mathrm{Li}}_3{\mathrm{BO}}_3$ (red circles) were obtained by refitting the data in Ref. [15] and for glassy ${\mathrm{Li}}_3{\mathrm{BO}}_3$ (green squares) were obtained by refitting the data in Ref. [31].

Figure 9

Plots of $\mathrm{MSD}(t,\langle T\rangle )$ from Eq. (10) in units of ${\AA }^2$ as a function of time in units of picosecond for $2\times 2\times 1$ supercells of ${\mathrm{Li}}_3{\mathrm{BN}}_2$ for the stoichiometric, I-int, I-vac, and C-doped models at average temperatures of $\langle T\rangle =1272,1259,1254,$ and 1261 K, respectively.

Figure 10

Plots of fractions of vacancies with respect to simulation time in units of picosecond for I-vac ${\mathrm{Li}}_3{\mathrm{BN}}_2$ at $\langle T\rangle =1155\mathrm{K}$ (purple) and 1200 K (red).

Figure 11

Plots of ${log}_{10}\left(\sigma T\right)$ vs $1000/T$ for the I-vac ${\mathrm{Li}}_3{\mathrm{BN}}_2$ (blue) and the C-doped ${\mathrm{Li}}_3{\mathrm{BN}}_2$ (orange). The data points were gathered from MD simulations and the straight line is a linear fit of the points with the slope determining the activation energy. The experimental results for polycrystalline ${\mathrm{Li}}_3{\mathrm{BN}}_2$ (red circles) were obtained by refitting the data in Ref. [30] and for glass-ceramic ${\mathrm{Li}}_3{\mathrm{BN}}_2$ (green squares) were obtained by refitting the data in Ref. [31].