  We propose a geometrical characterization of amorphous liquid structures that
suppress crystallization by competing locally with crystalline order. We
introduce for this purpose the crystal affinity of a liquid, a simple measure
of its propensity to accumulate local crystalline structures on cooling. This
quantity is explicitly related to the high temperature structural covariance
between local fluctuations in crystal order and that of competing liquid
structures: favouring a structure that, due to poor overlap properties,
anticorrelates with crystalline order reduces the affinity of the liquid. Using
a lattice model of a liquid, we show that this quantity successfully predicts
the tendency of a liquid to either accumulate or suppress local crystalline
fluctuations with increasing supercooling. We demonstrate that the crystal
affinity correlates strongly with the crystal nucleation rate and the
crystal-liquid interfacial free energy of the low-temperature liquid, making
our theory a predictive tool to determine easily which amorphous structures
enhance glass-forming ability.

Soft Condensed Matter