Why Melt? Melting Without High Temperature

From the post "Young And On Heat"

$F=4\pi E_s\Delta L=F_T=\sqrt{3}\rho D.\cfrac{\partial (d_s)}{\partial T}.\cfrac{1}{\alpha}$

We see that by driving the system with  varying   $T$,  we can set the system into resonance at

$f_{res}=\cfrac{1}{2\pi}\sqrt{\cfrac{4\pi E_s}{{4}\pi\rho}}$

where  $m={4}\pi\rho$,  a sphere of radius 1, mass per unit length,

$f_{res}=\cfrac{1}{2\pi}\sqrt{\cfrac{E_s}{\rho}}$

$E_s=\sqrt{3}E$

where  $E$ is the linear Young's Modulus and  $\sqrt{3}$  the 3D constant for the case of a sphere.

($E_s=E$ for the case of a rod.)

It might be that the sphere will melt at this thermal resonance frequency irrespective of the magnitude of the temperature.

If we consider that on increasing temperature, atoms in a solid vibrates at higher and higher frequency about its mean position in the solid lattice, this would suggest that at a particular temperature when the atoms are vibrating at this resonance frequency,  $f_{res}$,  the atom will simply break away from the lattice.  That is to say, the solid melts.

So melting is a case of the atoms vibrating at resonance frequency in heat.  And that it is possible to melt without high temperature but by applying  $T$  at the correct resonance frequency.