  We report on the frequency and stress dependence of the direct piezoelectric
d33 coefficient in BiFeO3 ceramics. The measurements reveal considerable
piezoelectric nonlinearity, i.e., dependence of d33 on the amplitude of the
dynamic stress. The nonlinear response suggests a large irreversible
contribution of non-180{\deg} domain walls to the piezoelectric response of the
ferrite, which, at present measurement conditions, reached a maximum of 38% of
the total measured d33. In agreement with this interpretation, both types of
non-180{\deg} domain walls, characteristic for the rhombohedral BiFeO3, i.e.,
71{\deg} and 109{\deg}, were identified in the poled ceramics using
transmission electron microscopy (TEM). In support to the link between
nonlinearity and non-180{\deg} domain wall contribution, we found a correlation
between nonlinearity and processes leading to deppining of domain walls from
defects, such as quenching from above the Curie temperature and
high-temperature sintering. In addition, the nonlinear piezoelectric response
of BiFeO3 showed a frequency dependence that is qualitatively different from
that measured in other nonlinear ferroelectric ceramics, such as "soft"
(donor-doped) Pb(Zr,Ti)O3 (PZT); possible origins of this dispersion are
discussed. Finally, we show that, once released from pinning centers, the
domain walls can contribute extensively to the electromechanical response of
BiFeO3; in fact, the extrinsic domain-wall contribution is relatively as large
as in Pb-based ferroelectric ceramics with morphotropic phase boundary (MPB)
composition, such as PZT. This finding might be important in the search of new
lead-free MPB compositions based on BiFeO3 as it suggests that such
compositions might also exhibit large extrinsic domain-wall contribution to the
piezoelectric response.
