Atomistic and electronic structure of antisite defects in yttrium aluminum garnet: Density-functional study

First-principles density-functional theory calculations have been performed on the atomistic structure, electronic structure, and distribution of antisite defects (AD) in yttrium aluminum garnet (YAG) ${\text{Y}}_3{\text{Al}}_5{\text{O}}_{12}$. The formations of one and two antisite defects per unit cell are endothermic and the formation energy per defect is lower in 2AD than in 1AD. In the most stable 1AD structure, Y and Al are as close as possible and two oxygen atoms become unbound to Al rising the energy of their (highest) valence levels and introducing a defect level in the gap 0.25 eV above the top of the perfect YAG valence band. The binding energy between the individual substitutional defects ${\text{Y}}_{\text{Al}}$ and ${\text{Al}}_{\text{Y}}$ to form 1AD is 0.74 eV. The most stable 2AD structure is made of two single ADs linked together with one ${\text{AlO}}_6$ moiety and it has basically the same electronic structure as the most stable 1AD; it is the only 2AD structure that preserves the inversion center with respect to the unit-cell center. In this case, the binding energy between two single ADs is 0.22 eV.

Figure 1

(Color online) Unit cell of YAG. The yttrium ions, the aluminum ions in quasioctahedral sixfold coordinations, and the ${\text{AlO}}_4$ quasitetrahedral moieties are indicated.

Figure 2

(Color online) Single substitutional defects. Top: Al atom in Y site [${\text{Al}}_{\text{Y}}$ orange (medium-light gray)]. Bottom: Y atom in ${\text{Al}}_{\text{oct}}$ site [${\text{Y}}_{\text{Al}}$ blue (medium-dark gray)]. First coordination shell (white oxygen atoms) and second coordination shell [black Y atoms, yellow (light gray) ${\text{Al}}_{\text{tet}}$ atoms, and red (dark gray) ${\text{Al}}_{\text{oct}}$ atoms] are shown. Oxygens labeled d1–d6 correspond to the original dodecahedral site and o1–o4 to the original octahedral site. Oxygens b1 and b2 will be bridge atoms between ${\text{Al}}_{\text{Y}}$ and ${\text{Y}}_{\text{Al}}$ in the most stable antisite defect (see below).

Figure 3

(Color online) The four possible 1AD:YAG, ordered according to the Y-Al distance before relaxation: (1) $3.39\text{Å}$, (2) $5.46\text{Å}$, (3) $6.94\text{Å}$, and (4) $8.16\text{Å}$. First coordination shell (white oxygen atoms) and, where appropriate, black Y atoms and yellow (light gray) ${\text{Al}}_{\text{tet}}$ shared atoms of the second coordination shell shown.

Figure 4

(Color online) Relaxed structure of the most stable 1AD:YAG [Fig. 3 (1)]. ${\text{Al}}_{\text{Y}}$ [orange (medium-light gray)], ${\text{Y}}_{\text{Al}}$ [blue (medium-dark gray)], and adjacent ${\text{Al}}_{\text{tet}}$ atoms [yellow (light gray)] shown. Oxygen labels according to Fig. 2.

Figure 5

(Color online) (a) Total DOS of YAG (black solid line), 1AD:YAG (red dashed line), and 2AD:YAG (blue dotted line). (b) Zoom over the gap zone. Vertical arrows indicate the end of the valence bands and the beginning of the conduction bands [same lines as in (a)]. (c) PDOS for the 1AD:YAG oxygen atoms shown in Fig. 4. (d) PDOS for the 2AD:YAG oxygen atoms shown in Fig. 8. In (c) and (d), dashed and dotted lines are used for the distinctive oxygens with indicated labels; thin lines are used for the remaining oxygens of the respective figures. The oxygen PDOS of perfect YAG is shown as a reference.

Figure 6

(Color online) Studied double 1AD:YAG with alternated ${\text{Y}}_{\text{Al}}$ positions. [111] axis shown. Positions before structural relaxation. Colors: ${\text{Al}}_{\text{Y}}$ atoms, orange (medium-light gray); ${\text{Y}}_{\text{Al}}$ atoms, blue (medium-dark gray); Y atoms, black; and ${\text{Al}}_{\text{oct}}$ atoms, red (dark gray).

Figure 7

(Color online) Studied double 1AD:YAG with contiguous ${\text{Y}}_{\text{Al}}$ positions. [111] axis shown. Positions before structural relaxation. Colors: ${\text{Al}}_{\text{Y}}$ atoms, orange (medium-light gray); ${\text{Y}}_{\text{Al}}$ atoms, blue (medium-dark gray); Y atoms, black; and ${\text{Al}}_{\text{oct}}$ atoms, red (dark gray).

Figure 8

(Color online) Relaxed structure of the most stable 2AD:YAG [Fig. 6 (A1)]. ${\text{Al}}_{\text{Y}}$ [orange (medium-light gray)], ${\text{Y}}_{\text{Al}}$ [blue (medium-dark gray)], and linking ${\text{Al}}_{\text{oct}}$ atom [red (dark gray)] shown. Oxygen labels according to Fig. 2.