  Earth's tectonic processes regulate the formation of continental crust,
control its unique deep water and carbon cycles, and are vital to its surface
habitability. A major driver of steady-state plate tectonics on Earth is the
sinking of the cold subducting plate into the underlying mantle. This sinking
is the result of the combined effects of the thermal contraction of the
lithosphere and of metamorphic transitions within the basaltic oceanic crust
and lithospheric mantle. The latter of these effects is dependent on the bulk
composition of the planet, e.g., the major, terrestrial planet-building
elements Mg, Si, Fe, Ca, Al, and Na, which vary in abundance across the Galaxy.
We present thermodynamic phase-equilibria calculations of planetary
differentiation to calculate both melt composition and mantle mineralogy, and
show that a planet's refractory and moderately-volatile elemental abundances
control a terrestrial planet's likelihood to produce mantle-derived,
melt-extracted crusts that sink. Those planets forming with a higher
concentration of Si and Na abundances are less likely to undergo sustained
tectonics compared to the Earth. We find only 1/3 of the range of stellar
compositions observed in the Galaxy is likely to host planets able to sustain
density-driven tectonics compared to the Sun/Earth. Systems outside of this
compositional range are less likely to produce planets able to tectonically
regulate their climate and may be inhospitable to life as we know it.
