Stability of intrinsic defects and defect clusters in $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$ from density functional theory calculations

A large experimental body of literature on lithium niobate, a technologically important ferroelectric, suggests that nonstoichiometric defects dominate its physical behavior, from macroscale switching to nanoscale wall structure. The exact structure and energetics of such proposed intrinsic defects and defect clusters remains unverified by either first-principles calculations or experiments. Here, density functional theory (DFT) is used to determine the dominant intrinsic defects in $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$ under various conditions. In particular, in an ${\mathrm{Nb}}_2{\mathrm{O}}_5$-rich environment, a cluster consisting of a niobium antisite compensated by four lithium vacancies is predicted to be the most stable defect structure, thereby verifying what was thus far a conjecture in the literature. Under ${\mathrm{Li}}_2\mathrm{O}$-rich conditions, the lithium Frenkel defect is predicted to be the most stable, with a positive defect formation energy (DFE). This is proposed as the underlying reason that the vapor-transport equilibration (VTE) method can grow stoichiometric $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$. The effects of temperature and oxygen partial pressure are also explored by combining the DFT results with thermodynamic calculations. These predictions provide a picture of a very rich defect structure in lithium niobate, which has important effects on its physical behavior at the macroscale.

Figure 1

(Color online) Schematic of possible defect arrangement involving one $\mathrm{Nb}_{\mathrm{Li}}{}^{\dots .}$ and four $V_{\mathrm{Li}}{}^{\prime }$ (so-called model III).

Figure 2

(Color online) The DOS for $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$.

Figure 3

(Color online) Difference in defect formation energy (relative to the $1\times 1\times 1$ system) as a function of system size. Supercell sizes of $1\times 1\times 1$, $2\times 1\times 1$, $2\times 2\times 1$, and $2\times 2\times 2$ correspond to 1, 2, 4, and 8 in the $x$ axis.

Figure 4

(Color online) Stability range of chemical potentials (in eV) of the elements in $\mathrm{Li}\mathrm{Nb}{\mathrm{O}}_3$. The region enclosed by points A, D, and ${\mathrm{P}}_{\mathrm{Li}\text{−}\mathrm{Nb}}$ satisfies Eq. (9), while the region enclosed by points B, C, ${\mathrm{P}}_{\mathrm{O}\text{−}\mathrm{Li}}$, and ${\mathrm{P}}_{\mathrm{O}\text{−}\mathrm{Nb}}$ satisfies Eq. (10). The intersection of these two regions defines the thermodynamically allowable range of chemical potentials. This stability region is thus defined by the shaded quadrilateral. Line AD represents using ${\mathrm{Li}}_2\mathrm{O}$ as reference state; line BC represents using ${\mathrm{Nb}}_2{\mathrm{O}}_5$ as reference. The oxygen partial pressure range (in atm) is that for room temperature.

Figure 5

(Color online) (a) Defect formation energies of various point defects as a function of Fermi energy; the lowest-energy charge state is given in each case. The Fermi energy ranges from $E_F=0$ (left) at the VBM to $E_F=3.5\mathrm{eV}$ at the conduction-band minimum (right). (b) Thermodynamic transition levels of O-related and Nb-related defects. The values under the line are with respect to the VBM. The transitions enclosed by squares have a negative $U$ character.

Figure 6

(Color online) Formation energies of neutral defects and defect clusters under ${\mathrm{Nb}}_2{\mathrm{O}}_5$-rich conditions (right=red) and ${\mathrm{Li}}_2\mathrm{O}$-rich conditions (left=blue).

Figure 7

(Color online) Defect stability range: in region AEFD, the Li-Frenkel is the dominant defect reaction, whereas in EBCF, the niobium antisite compensated by lithium vacancies is dominant. The Li-Frenkel is the dominant defect throughout the whole range of ${\mu }_{\mathrm{O}}$ along line AD, while the ${\mathrm{Nb}}_{\mathrm{Li}}^{\dots .}+4V_{\mathrm{Li}}{}^{\prime }$ cluster dominates along BC for all oxygen partial pressures.

Figure 8

(Color online) (a) The DFEs of $\mathrm{Nb}_{\mathrm{Li}}{}^{\dots .}+4V_{\mathrm{Li}}{}^{\prime }$, Li-Frenkel, and $V_{\mathrm{O}}{}^{..}+2V_{\mathrm{Li}}{}^{\prime }$ as a function of niobium chemical potential. (b) The defect concentration caused by $\mathrm{Nb}_{\mathrm{Li}}{}^{\dots .}+4V_{\mathrm{Li}}{}^{\prime }$, Li-Frenkel and $V_{\mathrm{O}}{}^{..}+2V_{\mathrm{Li}}{}^{\prime }$ as a function of niobium chemical potential.