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.