Superheating systematics of crystalline solids

Systematics of superheating ${\mathrm{(\theta =T/T}}_m\text{−1)}$ of crystalline solids as a function of heating rate $\mathrm{(Q)}$ are established as ${\text{β=A(Q)(θ+1)θ}}^2,$ where the normalized energy barrier for homogeneous nucleation is ${\text{β=16πγ}}_{\mathrm{sl}}^3{\text{/(3kT}}_m{\mathrm{\Delta H}}_m^2\mathrm{),}$ $T$ is temperature, $T_m$ melting temperature, $A$ a $Q$ -dependent parameter, ${\gamma }_{\mathrm{sl}}$ interfacial energy, ${\mathrm{\Delta H}}_m$ heat of fusion, and $k$ Boltzmann’s constant. For all elements and compounds investigated, β varies between 0.2 and 8.2. At 1 and ${10}^{12}\hspace{0.17em}\mathrm{K/s},$ $\text{A=60}$ and 31, $\text{θ=0.05–0.35}$ and 0.06–0.45, respectively. Significant superheating is achievable via ultrafast heating. We demonstrate that the degree of superheating achieved in shock-wave loading and intense laser irradiation as well as in molecular dynamics simulations ${\text{(Q∼10}}^{12}\hspace{0.17em}\mathrm{K/s})$ agrees with the $\mathrm{\theta –\beta –Q}$ systematics.