Ring-diffusion mediated homogeneous melting in the superheating regime

Homogeneous melting in the superheating regime is investigated by using molecular dynamics simulation of a Lennard-Jones model system. We show that the commonly observed catastrophic melting at the superheating limit is caused by fast heating rate. By keeping the system isothermally at temperatures below the superheating limit, we observe intense self-diffusion motions as the precursor of melting. The highly correlated atomic motions are related to the self-diffusion loops or rings. Two types of loops are observed, closed loop and open loop, where the latter is directly related to the homogeneous nucleation of the liquid phase. Homogeneous melting occurs when the number density of diffusion loops reaches a critical value. Our results suggest that homogeneous melting in the superheating regime is a first-order thermodynamic phase transition triggered by the self-diffusion loops when the kinetic constraint imposed by heating rate is lessened.

Figure 1

(Color online) Two types of interstitial sites in fcc crystals. The distance between the interstitial site [filled circle in green (gray)] and its nearest atom (filled circle in black) is indicated by a dashed line in each figure, where $a_0$ stands for the lattice constant. (a) Octahedral site and (b) tetrahedral site.

Figure 2

Atomic volume change during melting in gradual heating and isothermal heating methods. (a) Gradual heating method. The bottom $x$ axis shows the time from the beginning of the simulation, and the top $x$ axis shows the corresponding temperature at each time. $T_m^E$ stands for the normal (or equilibrium) melting point and $T_m^S$ represents the upper limit of superheating obtained at high heating rate. (b) Isothermal heating method. The isothermal heating starts at $T=0.739$. Three moments (marked by A, B, and C) are picked for investigation in Figs. 3, 4.

Figure 3

(Color online) Two-dimensional projected snapshots of the atomic configurations along the [100] direction at the three times marked in Fig. 2b. (a) At time A, $T=0.3$; (b) at time B, $T=0.739$ and before melting occurs; and (c) at time C, $T=0.739$ and after melting occurs.

Figure 4

(Color online) Pair distribution function (PDF) at the three times marked in Fig. 2b. Blue (black) short dash dot line: $T=0.3$ (time A). (b) Red (dark gray) solid line: $T=0.739$ and before melting occurs (time B). (c) Green (light gray) short dash line: $T=0.739$ and after melting occurs (time C).

Figure 5

Mean square displacement (MSD) in both gradual heating and isothermal heating methods. (a) Gradual heating. The bottom $x$ axis is the time, and the top $x$ axis is the temperature. The upper superheating limit is marked by $T_m^S$. (b) Isothermal heating method. The isothermal heating starts at $T=0.738$. No melting was observed in the isothermal regime despite of the large MSD. Three times (A–C) are picked for investigation in Fig. 6.

Figure 6

(Color online) Distributions of the atom displacements at different times [marked by A, B, and C in Fig. 5b] in the isothermal regime. The time is scaled to zero at the beginning of the isothermal regime. Blue (black) short dash line: after $0.025\mathrm{ns}$ from the beginning of isothermal heating; red (dark gray) short dot line: after $1.0\mathrm{ns}$; green (light gray) solid line: after $2.0\mathrm{ns}$.

Figure 7

The shortest interatomic distance as a function of time during the isothermal heating at $T=0.739$. The ideal distance between an octahedral interstitial site and its neighboring atom is indicated by $r_{\mathit{oct}\text{−}\mathit{\text{atom}}}$, and that between a tetrahedral interstitial site and its neighboring atom is indicated by $r_{\mathit{tet}\text{−}\mathit{\text{atom}}}$.

Figure 8

Evolution of the average number of the first nearest neighbors during the isothermal melting process at $T=0.739$. Five times (A–E) are picked for investigation as shown in Fig. 9.

Figure 9

(Color online) Distributions of the number of the first nearest neighbors at different times (marked by A–E in Fig. 8) during the isothermal melting process. time A: at $T=0.2$; time B: at $T=0.64$; time C: at $T=0.739$ and before melting occurs; time D: at $T=0.739$ and when melting occurs; time E: at $T=0.739$ and after melting occurs.

Figure 10

(Color online) Atom hopping in a crystal consisting of 500 atoms during the isothermal heating. The snapshots are 2D projections along the [110] direction. The smaller spheres in blue (black) represent the equilibrium atom positions. The bigger spheres in other colors represent hopping atoms. (a) Equilibrium atom positions and (b) clusters (indicated by bigger atoms) formed by the atom hopping. The vectors connect the equilibrium and new positions. The arrowheads of the vectors mark the new atom positions.

Figure 11

Schematic illustrations of two types of diffusion loops. (a) A closed diffusion loop and (b) an open diffusion loop.

Figure 12

(Color online) Four snapshots of forming a diffusion loop. The viewing angle is tilted slightly from the [110] direction. The blue (black) spheres represent original equilibrium sites. The red (dark gray) spheres represent the hopping atoms. The vectors represent the atom displacements and the arrowheads indicate the new atom positions. (a) At the beginning of forming a loop, (b) after $1.6\mathrm{ps}$, (c) after $4.4\mathrm{ps}$, and (d) after $6.1\mathrm{ps}$.

Figure 13

(Color online) Three-dimensional snapshots of the diffusion loops during the isothermal melting process. In order to illustrate the diffusion loops more clearly, only the atoms in the diffusion loops are shown. Different loops are distinguished by different colors. (a) At $t=0$ (the beginning of isothermal regime), (b) after $7.0\mathrm{ps}$, (c) after $9.0\mathrm{ps}$, and (d) after $9.2\mathrm{ps}$.

Figure 14

(Color online) Enthalpy change of each atom during the formation of the diffusion loops. Each sphere is colored according to its enthalpy. The bright green (light gray) is for low enthalpy (solidlike) atoms and the dark purple (dark gray) is for high enthalpy (liquidlike) atoms. The vectors represent the atom displacements and the arrowheads represent the actual atom positions. (a) At $t=0$, (b) after $7.0\mathrm{ps}$, (c) after $9.0\mathrm{ps}$, and (d) after $9.2\mathrm{ps}$.

Figure 15

(Color online) Open diffusion loops in a system of 4000 atoms at two isothermal temperatures: (a) $T=0.738$ and (b) $T=0.739\epsilon ∕k_B$. Atoms in the same color belong to the same loop.

Figure 16

(Color online) Evolution of the number of open loops at two isothermal temperatures. (a) Overall evolutions at $T=0.738$ and $T=0.739$ and (b) zoom-in view of the transition period enclosed by the blue rectangle.

Figure 17

Upper and lower bounds of the critical densities of defective atoms in various size systems.