  The temperature evolution of icosahedral medium-range order formed by
interpenetrating icosahedra in CuZr metallic glass-forming liquids was
investigated via molecular dynamics simulations. Scaling analysis based on
percolation theory was employed, and it is found that the size distribution of
clusters formed by the central atoms of icosahedra at various temperatures
follows a very good scaling law with the cluster number density scaled by
$S^{-\tau}$ and the cluster size $S$ scaled by $|1-T_c/T|^{-1/\sigma}$,
respectively. Here $T_c$ is scaling crossover-temperature. $\tau$ and $\sigma$
are scaling exponents. The critical scaling behaviour suggests that there would
be a structural phase transition manifested by percolation of locally favoured
structures underlying the glass transition, if the liquid could be cooled
slowly enough but without crystallization intervening. Furthermore, it is
revealed that when icosahedral short-range order (ISRO) extends to medium-range
length scale by connection, the atomic configurations of ISROs will be
optimized from distorted ones towards more regular ones gradually, which
significantly lowers the energies of ISROs and introduces geometric frustration
simultaneously. Both factors make key impacts on the drastic dynamic slowdown
of supercooled liquids. Our findings provide direct structure-property
relationship for understanding the nature of glass transition.
