Localization and delocationzation of surface disordering in surface mediated melting

Melting of solids usually starts with a thin liquid layer forming on the surface at temperatures below their bulk melting point. While the liquid phase formation in the so-called premelting is understood to be governed by the interface energies among the coexisting solid, liquid, and vapor phases, the influence of the underlying crystal structures on its kinetics, and atomistic mechanisms are unknown, and consequently, ignored in the theory of melting. Here we report the first observation of a strong influence of the underlying crystal structure on melting kinetics with the resulting localization and delocalization behavior of the surface disordering and the liquid layers. With increasing temperature, the surface disordering remains in the localized state with a constant thickness in fcc crystals, whereas it becomes delocalized by growing steadily into the bulk in bcc crystals. In both cases, the surface melting is found to occur with highly correlated atomic motion in the form of extended atomic chains and loops that emit from the disordered surface and transmit to the bulk. This newly discovered mechanism in surface melting is behind the surface melting kinetics: The close packed fcc crystal can effectively impede the correlated atomic motion and limit the surface disordering to only the localized region on surface, while the more openly packed bcc crystal allows for its proliferation by tunneling from the surface into the bulk of the crystals. These findings provide valuable insights for future development of new theories of crystal melting.

Figure 1

The Lindemann parameter ${\delta }_L$, the non-Gaussian parameter ${\alpha }_2$, and the structure factor S(k) for Cu (a) and Ta (b) with (100) surface versus temperature (bottom $x$ axis) and normalized temperature by the melting point (top x axis). Snapshots of the atomic configurations shown at different temperatures for fcc Cu at (a1) 800 K, (a2) 1050 K, (a3) 1356 K, and bcc Ta at (b1) 1500 K, (b2) 1911 K and (b3) 3080 K. (c) The structure factor S(k) and local ${\delta }_L$ for surface atoms versus normalized temperature by the bulk melting point for Cu and Ta. The surface disordering temperatures of Cu and Ta are labeled as $T_{\mathrm{Cu}}^{\mathrm{surf}\_\mathrm{dis}}$ and $T_{\mathrm{Ta}}^{\mathrm{surf}\_\mathrm{dis}}$, the premelting temperatures are $T_{\mathrm{Cu}}^{\mathrm{premelting}}$ and $T_{\mathrm{Ta}}^{\mathrm{premelting}}$, and the bulk melting temperature $T_m^{\mathrm{surf}}$.

Figure 2

The 2DRDFs for Cu (a) and Ta (b) at various temperatures.

Figure 3

The atomic number density profiles for Cu (a) and Ta (b) at different temperatures. As an illustration, we use the red arrow to mark the location of the interface between the liquid surface layer and the underlying crystal at 1358 K for Cu and at 3080 K for Ta. The bulk melting point is 1364 K for Cu and 3094 K for Ta in our MD simulations respectively. (c) The relation between the density of top 3 layers, shown in the light yellow regions in (a) and (b), versus temperature of Cu and Ta. (d) The zoom-ins of (c) close to the melting point.

Figure 4

(a) The thickness $\mathrm{\Delta }d$ of the surface disordered and liquid layers of Cu and Ta and (b) the liquid-solid interface velocity of Cu and Ta versus temperature during melting process. Since the length of the sample changes during heating, we normalize $\mathrm{\Delta }d$ by the length of sample at each temperature. Below premelting, $\mathrm{\Delta }d$ measures the disordered crystalline surface mean position.

Figure 5

The probability for particle displacement described by van Hove function $G_s\left(r,t\right)$ at 1099 K of Cu (a) and 2000 K of Ta (b) that are used to define mobile atoms.

Figure 6

The percentage of mobile atoms of the surface and bulk region for Cu (a) and Ta (b) versus temperature. The $x$ axis of temperature is also normalized by the respective melting temperature of Cu (1364 K) and Ta (3094 K).

Figure 7

The snapshots of the extended atomic configurations of the loops and chains that execute the correlated diffusive atomic motion on crystal lattices for the fcc Cu and bcc Ta with the (100) surface at different temperatures. At low temperatures, the EAC shows on the surface with top view for Cu at (a) $0.70T_m^{\mathrm{surf}}$ and (b) $0.75T_m^{\mathrm{surf}}$; and for Ta at (c) $0.60T_m^{\mathrm{surf}}$ and (d) $0.62T_m^{\mathrm{surf}}$, where $T_m^{\mathrm{surf}}$ is their bulk melting point in the samples with surfaces. At higher temperatures, the EACs appear inside the crystals which are plotted with the perspective view for Cu at (e) $0.90T_m^{\mathrm{surf}}$ and (f) $0.95T_m^{\mathrm{surf}}$; and for Ta at (g) $0.77T_m^{\mathrm{surf}}$ and (h) $0.80T_m^{\mathrm{surf}}$. To distinguish different chains and loops, we color them differently.

Figure 8

The total number of the extended atomic configurations in the forms of chains and loops versus normalized temperature $T/T_m^{\mathrm{surf}}$ ($x$ axis on the bottom of the figure) and time $t$ ($x$ axis on the top of figure in continuous heating of Cu (a) and Ta (b), where $T_m^{\mathrm{surf}}$ is their bulk melting point in the samples with surfaces.