Abstract: The existence of an off-centre distortion for impurities in cubic oxides is explored by Density Functional Theory calculations. We find that models based on ionic radii are inadequate to explain the off-centre instability. By contrast, increase of the nominal impurity charge or decrease of the host lattice constant act against the off-centre distortion. This explains why the motion of just the Ni2+ impurity can happen in SrO, in agreement with experimental data, while not for smaller Cr3+ or Ti4+ ions in the same lattice. Moreover, the different electronic structure and coupling to the host lattice are shown to be behind a small but positive force constant for Na+ and Mn2+ in SrO. Our results indicate that an off-centre motion in MgO:Ni2+ is rather unlikely and that the local contributions to the instability in pure BaTiO3 are not enough to induce ferroelectricity if just the movement of Ti4+ ion is considered.

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