Pressure-induced decomposition of binary lanthanum intermetallic compounds

We present a comprehensive study on structural and electronic properties of lanthanum intermetallic compounds ($M_x{\mathrm{La}}_y$, $M=\text{Be}$, Mg, Al, Ga, In, Tl, Pb, and Bi) under high pressure. By using a swarm intelligence structure search method combined with first-principles calculations, pressure-induced phase transitions of $M_x{\mathrm{La}}_y$ were investigated, with several new structures predicted. A universal yet intriguing phenomenon was found; that is, all of these compounds will decompose into elemental solids at certain pressures, which is against the general intuition that extreme pressure always stabilizes and densifies materials. Mechanical analysis suggests that this anomalous behavior is associated to the elastic moduli and interatomic interaction in $M_x{\mathrm{La}}_y$, and their changes under extreme pressure. A low bulk modulus and larger atomic volume of La result in a smaller volume for the elemental mixture compared to their compound at high pressures, which leads to an energetically favorable $PV$ work and enthalpy for the elemental mixture. Furthermore, the external pressure tends to weaken the La-$M$ electrostatic interaction in compounds as evidenced by the reduced charge transfer between La and $M$, which in turn modifies the electronegativity of La and $M$ and destabilizes the compounds. Our results shed light on the high-pressure behaviors of La-based intermetallic compounds and provide important guidance for understanding other La-like intermetallic compounds at high pressures.

Figure 1

Thermodynamic stabilities with respect to $M$ and La, and phase diagrams of various compounds (a) ${\mathrm{Be}}_x{\mathrm{La}}_y$, (b) ${\mathrm{Mg}}_x{\mathrm{La}}_y$, (c) ${\mathrm{Al}}_x{\mathrm{La}}_y$, (d) ${\mathrm{Ga}}_x{\mathrm{La}}_y$, (e) ${\mathrm{In}}_x{\mathrm{La}}_y$, (f) ${\mathrm{Tl}}_x{\mathrm{La}}_y$, (g) ${\mathrm{Pb}}_x{\mathrm{La}}_y$, and (h) ${\mathrm{Bi}}_x{\mathrm{La}}_y$ at 0 K and different pressures. The stoichiometries of structures lying on the convex hull (solid line) are stable against decomposition at a given pressure, while those located above the convex hull (dashed line) are either unstable or metastable. The stoichiometries studied here are experimentally known at ambient pressure.

Figure 2

The convex hulls of different stoichiometries of (a) ${\mathrm{Mg}}_x{\mathrm{La}}_y$ and (b) ${\mathrm{Al}}_x{\mathrm{La}}_y$ compounds at 0, 50, 100, 200, and 300 GPa. All of the studied phases are unstable at pressures above 100 GPa.

Figure 3

$\mathrm{\Delta }H$, $\mathrm{\Delta }U$, and $P\mathrm{\Delta }V$ versus pressure for (a) ${\mathrm{Al}}_2\mathrm{La}$, Al $+$ La mixture, and (b) ${\mathrm{Ga}}_2\mathrm{La}$, Ga $+$ La mixture, where Al (Ga) $+$ La is chosen as the reference. Here, the dashed lines represent the decomposition pressure. ${\mathrm{Al}}_2\mathrm{La}$ decomposes at around 80 GPa, while ${\mathrm{Ga}}_2\mathrm{La}$ decomposes at around 350 GPa.

Figure 4

(a), (b) The volume differences between the compound (${\mathrm{Al}}_2\mathrm{La}$, ${\mathrm{Ga}}_2\mathrm{La}$) and La $+$ M (M= Al, Ga) are shown in figure a, b, respectively. As earlier, the dashed line represents the decomposition pressure. (c), (d) The $\mathrm{\Delta }\mathrm{V}$ ($\mathrm{\Delta }\mathrm{V}$ = ${\mathrm{V}}_{\mathrm{pressure}}$–${\mathrm{V}}_0)$ of ${\mathrm{Al}}_2\mathrm{La}$ and ${\mathrm{Ga}}_2\mathrm{La}$ versus pressure are shown in figure c, d, respectively. ${\mathrm{V}}_0$ represents the volume at 0 GPa.

Figure 5

The Bader charge of La in (a) ${\mathrm{Al}}_2\mathrm{La}$ from 0 to 100 GPa and (b) ${\mathrm{Ga}}_2\mathrm{La}$ from 0 to 400 GPa. The charge transfer decreases almost linearly with increasing pressures, which means that the interaction between Al (Ga) and La gradually decreases at high pressures.

Figure 6

Calculated (a), (b) PDOS and (c), (d) pCOHP for (a), (c) ${\mathrm{Al}}_2\mathrm{La}$ at 80 GPa and (b), (d) ${\mathrm{Ga}}_2\mathrm{La}$ at 350 GPa. The states are aligned at the Fermi level (vertical dashed lines).

Figure 7

(a) The $\mathrm{\Delta }H$, $\mathrm{\Delta }U$, $P\mathrm{\Delta }V$ versus pressure for ${\mathrm{Al}}_2\mathrm{Y}$ and $\mathrm{Al}+\mathrm{Y}$ mixtures, where $\mathrm{Al}+\mathrm{Y}$ is chosen as the reference. (b) The Bader charge of ${\mathrm{Al}}_2\mathrm{Y}$ from 0 to 250 GPa. As earlier, the dashed line represents the decomposition pressure. ${\mathrm{Al}}_2\mathrm{Y}$ decomposes at about 215 GPa.