First-principles thermodynamic modeling of lanthanum chromate perovskites

Tendencies toward local atomic ordering in (A,A′)(B,B′)O${}_{3-\delta }$ mixed composition perovskites are modeled to explore their influence on thermodynamic, transport, and electronic properties. In particular, dopants and defects within lanthanum chromate perovskites are studied under various simulated redox environments. (La${}_{1-x}$,Sr${}_x$)(Cr${}_{1-y}$,Fe${}_y$)O${}_{3-\delta }$ (LSCF) and (La${}_{1-x}$,Sr${}_x$)(Cr${}_{1-y}$,Ru${}_y$)O${}_{3-\delta }$ (LSCR) are modeled using a cluster expansion statistical thermodynamics method built upon a density functional theory database of structural energies. The cluster expansions are utilized in lattice Monte Carlo simulations to compute the ordering of Sr and Fe(Ru) dopant and oxygen vacancies (Vac). Reduction processes are modeled via the introduction of oxygen vacancies, effectively forcing excess electronic charge onto remaining atoms. LSCR shows increasingly extended Ru-Vac associates and short-range Ru-Ru and Ru-Vac interactions upon reduction; LSCF shows long-range Fe-Fe and Fe-Vac interaction ordering, inhibiting mobility. First principles density functional calculations suggest that Ru-Vac associates significantly decrease the activation energy of Ru-Cr swaps in reduced LSCR. These results are discussed in view of experimentally observed extrusion of metallic Ru from LSCR nanoparticles under reducing conditions at elevated temperature.

Figure 1

Bader analysis derived effective charges for LSCF structures with variable Cr, Fe, and O-Vac content. (a) Fixed La${}_{0.67}$Sr${}_{0.33}$ concentration, (b) Fixed La${}_{1.0}$ concentration. Units are electron/atom, $e$; positive effective charge is electron deficient, i.e., cationic.

Figure 2

Bader analysis derived effective charges for LSCR structures with variable Cr, Ru and O-Vac content. (a) Fixed La${}_{0.67}$Sr${}_{0.33}$ concentration, (b) Fixed La${}_{1.0}$ concentration.

Figure 3

Partial densities of states for LSCF with fixed La${}_{0.67}$Sr${}_{0.33}$ Cr${}_{0.67}$Fe${}_{0.33}$ composition and varying O-Vac content. (a) O${}_3$ and (b) O${}_{2.67}$.

Figure 4

Partial densities of states for LSCR with composition La${}_{0.67}$Sr${}_{0.33}$Cr${}_{0.67}$Ru${}_{0.33}$ and variable O-Vac content. (a) O${}_3$, (b) O${}_{2.67}$.

Figure 5

Vac-Vac interactions sequentially ordered by coordination shell for (a) LSCF and (b) LSCR with anion equilibration. δ refers to the value in the chemical formulas for LSCF and LSCR found within Sec. 1. Vertical axis represents deviation from the expected random distribution value as a percentage of each shell's coordination number.

Figure 6

Sr-Vac interactions sequentially ordered by coordination shell for (a) LSCF and (b) LSCR with unrestricted equilibration.

Figure 7

Sr-Sr interactions sequentially ordered by coordination shell for (a) LSCF and (b) LSCR with unrestricted equilibration.

Figure 8

B′-Sr interactions sequentially ordered by coordination shell for (a) LSCF and (b) LSCR, both with unrestricted equilibration.

Figure 9

B′-B′ interactions sequentially ordered by coordination shell for (a) LSCF and (b) LSCR with unrestricted equilibration.

Figure 10

B′-Vac interactions sequentially ordered by coordination shell for (a) LSCF and (b) LSCR with both anion and B-site equilibration.

Figure 11

Random Ru and equilibrated oxygen vacancy positions of a 20 × 20 × 20 cell in the “anion-only” equilibration model at 1000 K. Small and blue: Ru; large and red: oxygen vacancy.

Figure 12

2D Ru-Vac associates sampled from structure seen in Fig. 11 with (a) three and (b) two nearest-neighbor oxygen vacancies. Arrows denote a proposed coordinated diffusion mechanism aiding the swap of Ru and Cr atoms. Tiny/green: Cr, Small/blue: Ru, Medium/purple: O, Large/red: oxygen vacancy.