Systematics of superheating ( ϭT/T m Ϫ1) of crystalline solids as a function of heating rate (Q) are established as ϭA(Q)( ϩ1) 2 , where the normalized energy barrier for homogeneous nucleation is ϭ16 ␥ sl 3 /(3kT m ⌬H m 2 ), T is temperature, T m melting temperature, A a Q-dependent parameter, ␥ sl interfacial energy, ⌬H m heat of fusion, and k Boltzmann's constant. For all elements and compounds investigated,  varies between 0.2 and 8. Superheating ( ϭT/T m Ϫ1) of a crystalline solid occurs when the long-range order of the crystalline structure is maintained up to certain temperature T above the equilibrium melting temperature T m . Previously, the details of crystal melting and the temperature range over which solids may be superheated have been investigated. [1][2][3][4][5][6][7] In contrast to undercooling of liquid prior to crystallization, experimental superheating of crystals is difficult as grain boundaries and free surfaces lower the energy barriers for melt nucleation. 8,9 Special experimental designs 5 and rapid heating are required to superheat crystalline solids. Catastrophic melting 1,2 and homogeneous nucleation 3,4 theories have been utilized to define the limits of superheating, and a wide range of superheating ( ϳ0.1-2.0) is predicted. Here, we will investigate the systematics of nucleation energy barrier for elements and compounds, and the corresponding superheating as a function of heating rate. We also compare theory to superheating achieved in experiments and simulations.Homogeneous nucleation of melt may be described via classical theories. 9-14 Let I be the rate per unit volume of steady-state homogeneous nucleation of melt in solid: 14,15 IϭI 0 exp ͩ Ϫ ⌬G c kT ͪ ,
͑1͒where ⌬G c is the critical Gibbs free energy for nucleation, and k is Boltzmann's constant. then I can be written as IϭI 0 f (, ), withNucleation rate I is controlled by f (, ), essentially by  at a given temperature. Equations ͑1͒-͑3͒ are also applicable to the undercooling case.To estimate the magnitude of , we note that ␥ sl ϳ0.1 J/m 2 , T m ϳ10 3 K and ⌬H m ϳ10 9 J/m 3 , yields  ϳ1.2. Based on previous data, 14  for elements is calculated ͑Fig. 1͒. For Group IVB-IIB elements,  is 0.9-3.1, except for Hg ͑6.3͒. For most transition metals, ϳ1.8. Due to the unproportionally lower ⌬H m and T m , Group IIIA-VIA elements have larger  values ͑2.5-8.2͒ except Al ͑1.5͒ and Se ͑0.2͒. Figure 1 demonstrates the periodic nature of  for elements due to their periodic variations in electronic structure, with peaks occurring mostly at Group IIIA-VIA elements and Hg.  for compounds such as some alkali halides and silicates is similar. In general, ␥ sl increases with T m and ⌬H m , because ␥ sl , T m , and ⌬H m are fundamentally related to binding energy. Thus, although  is sensitive to ␥ sl , varia-