Fragility and thermal expansion control crystal melting and the glass transition

Analytical relations for the glass transition temperature, Tg, and the crystal melting temperature, Tm, are developed on the basis of nonaffine lattice dynamics. The proposed relations explain the following: (i) the seemingly universal factor of ≈2/3 difference between the glass transition temperature and the melting temperature of the corresponding crystal, and (ii) the recent empirical discovery that both Tg and Tm are proportional to the liquid fragility m divided by the thermal expansion coefficient α of the solid.