  The gas-phase metallicity distribution has been analyzed for the hot
atmospheres of 29 galaxy clusters using {\it Chandra X-ray Observatory}
observations. All host brightest cluster galaxies (BCGs) with X-ray cavity
systems produced by radio AGN. We find high elemental abundances projected
preferentially along the cavities of 16 clusters. The metal-rich plasma was
apparently lifted out of the BCGs with the rising X-ray cavities (bubbles) to
altitudes between twenty and several hundred kiloparsecs. A relationship
between the maximum projected altitude of the uplifted gas (the "iron radius")
and jet power is found with the form $R_{\rm Fe} \propto P_{\rm jet}^{0.45}$.
The estimated outflow rates are typically tens of solar masses per year but
exceed $100 ~\rm M_\odot ~yr^{-1}$ in the most powerful AGN. The outflow rates
are 10% to 20% of the cooling rates, and thus alone are unable to offset a
cooling inflow. Nevertheless, hot outflows effectively redistribute the cooling
gas and may play a significant role at regulating star formation and AGN
activity in BCGs and presumably in giant elliptical galaxies. The metallicity
distribution overall can be complex, perhaps due to metal rich gas returning in
circulation flows or being blown around in the hot atmospheres. Roughly 15% of
the work done by the cavities is expended lifting the metal-enriched gas,
implying their nuclear black holes have increased in mass by at least $\sim
10^7$ M$_\odot$ to $10^9$ M$_\odot$. Finally, we show that hot outflows can
account for the broad, gas-phase metallicity distribution compared to the
stellar light profiles of BCGs, and we consider a possible connection between
hot outflows and cold molecular gas flows discovered in recent ALMA
observations.
