Stabilization of the amorphous phase inside carbon nanotubes - solidification in a constrained geometry

We present an explanation for the observation of Ajayan and Iijima in 1993 that liquid lead inside carbon nanotubes of small diameters remains discovered, whereas inside tubes of larger diameters it crystallizes. We show that there exists a critical radius for the nanotubes such that in the tubes of smaller radius the amorphous phase is stabilized. Our analysis also leads to a novel way of estimating a lower bound of the free energy for the solid-liquid interface