  It is currently unknown if neutron stars (NSs) are composed of nucleons only
or are hybrid stars, i.e., in addition to nucleonic crusts and outer cores,
they also possess quark cores. Quantum chromodynamics allows for such a
possibility, but accurate calculations relevant for compact stars are still
elusive. Here we investigate some crust-breaking aspects of hybrid stars. We
show that the crust-breaking frequency and maximum fiducial ellipticity are
sensitive to the quark-hadron density jump and equation of state stiffness.
Remarkably, the crust-breaking frequency related to static tides scales
linearly with the mass of the star (for a given companion's mass), and its
slope encompasses information about the microphysics of the star. However, for
precise crust-breaking frequency predictions, relativistic corrections to
Kepler's third law and the Newtonian tidal field should not be ignored. When a
liquid quark core touches an elastic hadronic phase (the result of a
significant energy-density jump), the maximum ellipticity can increase around
an order of magnitude when compared to a liquid quark core touching a liquid
hadronic phase. That is relevant because it would increase the odds of
detecting continuous gravitational waves from NSs. Our order-of-magnitude
analysis also suggests that a given upper limit to the
ellipticity(crust-breaking frequency) could have representatives in stars with
either small or intermediate(large) energy-density jumps. Therefore, when upper
limits to the ellipticity for isolated stars are better constrained or
electromagnetic radiation (e.g., gamma-ray precursors) is detected along with
gravitational waves in inspiraling binary systems, they may help constrain some
aspects of phase transitions in NSs.
