Structures, Li${}^{+}$ mobilities, and interfacial properties of solid electrolytes Li${}_3$PS${}_4$ and Li${}_3$PO${}_4$ from first principles

This work reports a computer modeling comparison of two solid electrolyte materials, Li${}_3$PO${}_4$ and Li${}_3$PS${}_4$, in terms of the bulk structures, Li ion mobilities, and their interface properties with vacuum and with Li metal. The simulations show that for some forms of Li${}_3$PS${}_4$, Li ions can move from a host lattice site to an interstitial site with negligible net energy change. This favorable process for the formation of vacancy-interstitial pairs is undoubtedly important for the structural and ion migration properties of $\beta$-Li${}_3$PS${}_4$. Our model results for the idealized interfaces between the electrolytes and Li metal show that Li${}_3$PO${}_4$ /Li interfaces are stable, while Li${}_3$PS${}_4$ /Li interfaces are not. We find that a Li${}_3$PS${}_4$ surface in the presence of a small amount of Li relaxes to a complicated structure involving broken P-S bonds. On the other hand, the computer models show that a very thin film of Li${}_2$S on the Li${}_3$PS${}_4$ surface can provide a protective buffer layer to stabilize the interface between the Li${}_3$PS${}_4$ electrolytes and the Li metal anode.

Figure 1

Ball and stick diagram of the unit cell of the $Pmn{2}_1$ structure of $\gamma$-Li${}_3$PS${}_4$. The Li, P, and S sites are depicted with gray, black, and yellow balls, respectively. The roman “$a$” and “$b$” indicate examples of Li sites with those Wyckoff labels.

Figure 2

Ball and stick diagram of the unit cell of $Pnma$ structure of $\gamma$-Li${}_3$PO${}_4$. The P and O sites are depicted with black and blue balls, respectively. The Li sites are shown with gray and green balls for the Wyckoff “$d$” and “$c$” sites, respectively.

Figure 3

Ball and stick diagram of the unit cell of $Pnma$ structures of Li${}_3$PS${}_4$. The P and S sites are depicted with black and yellow balls, respectively. The Li sites are shown with gray balls for the Wyckoff d sites. The pink balls correspond to the $b$ sites occupied in the $\beta$-Li${}_3$PS${}_4$-$b$ structure while the green balls correspond to the $c$ sites occupied in the $\beta$-Li${}_3$PS${}_4$-$c$ structure.

Figure 4

Ball and stick diagram of $\beta$-Li${}_3$PO${}_4$ with superposed interstitial sites. The Li, P, and O sites are depicted with gray, black, and blue balls respectively. The equivalent positions for the $I$, $II$, and $I_1$ sites are depicted with pink, green, and orange balls respectively.

Figure 5

Energy diagram for Li vacancy migration along the $\mathbf{a}$ and $\mathbf{c}$ axes for $\gamma$-Li${}_3$PS${}_4$. The energy scale is taken to be the same as that given in Table ; that is, zero energy is referenced to the configuration for the Li vacancy at a site of type $a$.

Figure 6

Ball and stick diagram of $\beta$-Li${}_3$PS${}_4$-$b$ structure using the same convention used in Fig. 3 except the Li sites of the perfect lattice are indicated with gray balls, while the low-energy interstitial sites (having “$c$” symmetry) are indicated with green balls. The site labels are used to indicate possible vacancy migration paths.

Figure 7

Energy diagram of NEB path for Li vacancy migration along the $\mathbf{a}$ axis for $\beta$-Li${}_3$PS${}_4$-$b$. The energy scale is zeroed at the configuration for the Li vacancy at the $d$ site.

Figure 8

Energy diagram of NEB path for Li vacancy migration along the $\mathbf{b}$ and $\mathbf{c}$ axes for $\beta$-Li${}_3$PS${}_4$-$b$.

Figure 9

Plot of $\Delta H_{\mathrm{total}}$ versus surface area $A$ for slab calculations of various structures of Li${}_3$PS${}_4$ with various slab thicknesses. The lines correspond to Eq. (5). The integers in parentheses indicate the number of unit cell layers in each of the simulation slabs.

Figure 10

Ball and stick representation of optimized structure of an ideal [010] slab of $\beta$-Li${}_3$PO${}_4$ with several layers of Li. The supercell contains four formula units of $\beta$-Li${}_3$PO${}_4$ and 14 Li atoms. The Li, P, and O sites are depicted with gray, black, and blue balls, respectively.

Figure 11

Partial density of states plot of $\beta$-Li${}_3$PO${}_4$ electrolyte in the Li presence of Li layers as shown in Fig. 10. The energy scale for the plot was adjusted to the top of the filled valence band of the $\beta$-Li${}_3$PO${}_4$ layer. The weight factors for the partial densities of states are given by Eq. (2) for each type of atomic site $a$, averaged over sites of the same type.

Figure 12

Ball and stick representation of Li${}_3$PS${}_4$ surfaces with Li, P, and S sites depicted with gray, black, and yellow balls, respectively. (a) Ideal [010] slab of $\gamma$-Li${}_3$PS${}_4$ with initial position of Li atoms. The supercell contains four formula units of $\gamma$-Li${}_3$PS${}_4$ and four Li atoms. (b) Relaxed structure of configuration (a).

Figure 13

(a) Relaxed structure of a [010] slab of $\gamma$-Li${}_3$PS${}_4$ with buffer layers of Li${}_2$S. The supercell contains four units of Li${}_3$PS${}_4$ and eight units of Li${}_2$S. (b) Relaxed structure of buffered electrolyte shown in (a) with the addition of 14 Li atoms in the supercell.

Figure 14

Partial density of states plot of $\gamma$-Li${}_3$PS${}_4$ electrolyte, buffered with Li${}_2$S in the presence of Li layers as shown in Fig. 13b. The upper panel shows the states associated with the $\gamma$-Li${}_3$PS${}_4$ and the lower panel shows the states associated with the Li${}_2$S buffer layer. Both panels show the contributions from the metallic Li layer. The energy scale for the plot was adjusted to the top of the filled valence band of the $\gamma$-Li${}_3$PS${}_4$ layer. The weight factors for the partial densities of states are given by Eq. (2) for each type of atomic site $a$, averaged over sites of the same type.