Atomistic Simulation of Dopant Incorporation in Barium Titanate

The results of an atomistic simulation study on the incorporation of ions of the first series of transition metals (Cr 3+, Cr 4+, Fe 2+, Fe 3+, Co 2+, Co 3+, Ni 2+, and Ni 3+), Y 3+, and ions of the lanthanide series (Er 3+, Gd 3+, Tb 3+, Pr 3+, Pr 4+, and La 3+) in the BaTiO 3 lattice are presented and discussed. The ions of the transition metals prefer to substitute at the titanium site with oxygen-vacancy compensation. For iron and cobalt, oxidation from the divalent to the trivalent state during incorporation is favored. Nickel and chromium are preferentially incorporated in the valence state 2+ and 3+, respectively. Formation of stable defect pairs with different types of lattice defects is predicted for the transition-metal impurities. For La 3+ and Pr 3+, substitution occurs at the barium site, whereas Y 3+, Tb 3+, Gd 3+, and Er 3+ tend to simultaneous substitution on both cation sites. Formation of dopant-titanium-vacancy pairs is predicted for the rare-earth ions and Y 3+. The effect of doping on the lattice parameter of c-BaTiO 3 has been studied by a mean-field calculation. Comparison with experimental data confirms the dependence of the preferred substitution site on the ionic radius of the impurity. For dopants with intermediate size (Y 3+, Er 3+, Tb 3+, and Gd 3+), the Ba/Ti ratio is important in the incorporation mechanism.