LiB and its boron-deficient variants under pressure

Results of computational investigations of the structural and electronic properties of the ground states of binary compounds LiB${}_x$ with 0.67 ≤ $x$ ≤ 1.00 under pressure are reported. Structure predictions based on evolutionary algorithms and particle swarm optimization reveal that with increasing pressure, stoichiometric 1:1-LiB undergoes a variety of phase transitions, is significantly stabilized with respect to the elements and takes up a diamondoid boron network at high pressures. The Zintl picture is very useful in understanding the evolution of structures with pressure. The experimentally seen finite range of stability for LiB${}_x$ phases with 0.8 ≤ $x$ ≤ 1.00 is modeled both by boron-deficient variants of the 1:1-LiB structure and lithium-enriched intercalation structures. We find that the finite stability range vanishes at pressures $P$ ≥ 40GPa, where stoichiometric compounds then become more stable. A metal-to-insulator transition for LiB is predicted at $P$ $=$ 70 GPa.

Figure 1

LiB crystal structure, as proposed by Liu et al.[32] The unit cell is indicated, and big red/dark gray (small green/light gray) spheres denote Li (B) atoms. (Left) Side view, emphasizing boron chains. (Right) Top view, emphasizing mixed Li-B graphitic sheets.

Figure 2

The R-3m “metal sandwich” structure of LiB, shown at $P$ $=$ 1 atm in the hexagonal unit cell.

Figure 3

Relative enthalpies of formation of various LiB phases in the ground state. Inset shows the NaTl structure type for LiB, structure optimized at $P$ $=$ 80 GPa.

Figure 4

Electronic DOS of various ground states LiB phases, all at $P$ $=$ 80 GPa. From left: $P{\mathit{6}}_{\mathit{3}}$/mmc, R-3m, and Fd-3m structures. The evolution of the DOS at the Fermi level with increased pressure is shown on the right.

Figure 5

Electronic band structures for various LiB phases. From left to right: $P{\mathit{6}}_{\mathit{3}}$/mmc, R-3m, and Fd-3m structures, all at $P$ $=$ 80 GPa. The hexagonal unit cell for R-3m and the conventional unit cell for the Fd-3m structure were used.

Figure 6

(Left) Ground-state enthalpies of formation for boron-deficient LiB${}_x$ structures, relative to the elements; (middle) relative internal energies for the same structures; (right) relative $pV$ terms for the same structures. (Left) Dashed lines are quadratic fits to the enthalpies; (middle and right), lines are guide to the eye only.

Figure 7

(Left) Ground-state Li${}_5$B${}_4$ phase in the Li${}_5$Ga${}_4$ structure, (right) the Li${}_3$B${}_2$ phase in the Li${}_3$Al${}_2$ structure. Both are shown at $P$ $=$ 1 atm.

Figure 8

Ground-state enthalpies of formation for various boron chain structures (filled symbols, dashed lines) and sandwich structures (open symbols, solid lines), at various pressures. Dashed lines are quadratic fits (same as in Fig. 6), solid lines are cubic spline fits.

Figure 9

(Top) Stability range for ground-state boron chain structures as a function of pressure, indicated as the shaded area. The inset shows how the data points are acquired, here for the $P$ $=$ 20 GPa phase diagram: dashed and solid red lines are chain and sandwich enthalpy curves (see Fig. 8), solid black line is the convex hull, including part of the chain structure parabola. Two plots on the bottom compare the $c/a$ ratio and $c$ axis for various chain stoichiometries (labeled by $x$ in LiB${}_x$) with experimental results from Ref. 36.

Figure 10

Electronic band structure (left, $P$ $=$ 1 atm, and middle, $P$ $=$ 80 GPa) and DOS (right, $P$ $=$ 80 GPa) for the P-3m1 ground-state structure of Li${}_5$B${}_4$.

Figure 11

Electronic band structure (left, $P$ $=$ 1 atm, and middle, $P$ $=$ 80 GPa) and DOS (right, $P$ $=$ 80 GPa) for the R-3m ground-state structure of Li${}_3$B${}_2$. The hexagonal unit cell was used for the band structures.

Figure 12

Ground-state enthalpies of formation for the LiB, Li${}_5$B${}_4$, and Li${}_3$B${}_2$ structures relative to the elemental crystals as a function of pressure. Dashed lines are the enthalpies of the convex hull for the respective stoichiometries, as obtained from our calculations.