Model for diffusion at the microcanonical superheating limit from atomistic computer simulations

The diffusion statistics of atoms in a crystal close to the critical superheating temperature was studied in detail using molecular dynamics and Monte Carlo simulations. We present a continuous random-walk model for diffusion of atoms hopping through thermal vacancies. The results obtained from our model suggest that the limit of superheating is precisely the temperature for which dynamic percolation happens at the time scale of a single individual jump. A possible connection between the critical superheating limit and the maximization of the Shannon entropy associated with the distribution of jumps is suggested. As a practical application of our results, we show that an extrapolation of the critical superheating temperature (and therefore an estimation of the melting point) can be performed using only the dynamical properties of the solid state.

Figure 1

Example of the application of the Z method to determine the melting temperature. The relation between $T_m$ (lower point of the Z-shaped isochoric curve) and $T_{\text{LS}}$ (higher point) is shown for an embedded atom solid.

Figure 2

Mean-square displacement for a time interval up to 2.5 ns, computed for the EAM solid at $T=7000\text{K}=0.75T_{\text{LS}}$.

Figure 3

Mean-square displacement exponent $\gamma$ as a function of temperature for the LJ and EAM solids.

Figure 4

Average radial distribution function $g\left(r\right)$ computed for the EAM solid at $T=7000\text{K}=0.75T_{\text{LS}}$.

Figure 5

Mean-square displacement computed for the LJ solid at $T=6200\text{K}=0.99T_{\text{LS}}$ with Creutz’s microcanonical MC algorithm.

Figure 6

Velocity autocorrelation function (VACF) for different temperatures approaching the superheating limit $T_{\text{LS}}$. The inset shows the time scale corresponding to atomic vibrations.

Figure 7

Vibrational density of states for different temperatures approaching the superheating limit $T_{\text{LS}}$.

Figure 8

Comparison between superheated and liquid vibrational properties. Left, velocity autocorrelation function. Right, vibrational density of states.

Figure 9

Mobility histograms $J_{\tau }\left(r\right)$ obtained from molecular-dynamics simulations of an EAM solid close to $T_{\text{LS}}$.

Figure 10

Mobility components for the simple random walk in a square lattice.

Figure 11

Mobility components for the vacancy-mediated random walk in a square lattice.

Figure 12

Comparison between the $J_i$ curves as a function of observation time for Lennard-Jones MD (Ar, 108 atoms) and the MC geometrical model.

Figure 13

(a) Instantaneous temperature as a function of time during melting. (b) Jump diffusion components as a function of time.

Figure 14

Mobility components computed from MD simulations as a function of the normalized observation time $\tau /{\tau }_0$, (a) at $T<T_{\text{LS}}$ in the solid isochore, (b) at $T_{\text{LS}}$, and (c) in the liquid isochore. The dotted line $J=1/3$ is drawn for clarity.

Figure 15

Characteristic observation times ${\tau }_0$ and ${\tau }_1$ on increasing temperatures, close to $T_{\text{LS}}$. The star corresponds to the measured $T_{\text{LS}}$ and $\tau ={\tau }_D$.