Time-dependent temperature and pressure in four independent simulation runs, showing homogeneous melting from superheated hcp solid Fe in a system of 7776 atoms. All four simulations were initiated from perfect crystal positions, with initial random velocities corresponding to the same temperature T m = 15 600 K, the mean quasi-steady temperatures of the superheated solid and the final liquid being T sol = 7590 K and T liq = 6315 K.
Histograms of waiting times τw before the transition to liquid constructed from repeated simulations at two initial temperatures for the system of 7776 atoms. Histograms shown by dashed (red) and solid (black) lines result from initial temperatures of T i = 15 800 and 16 000 K, respectively, the quasi-steady solid and liquid temperatures in the two cases being T sol = 7640 and 7740 K and T liq = 6410 and 6505 K. Dashed and dotted curves show exponential functions fitted to histograms (see text).
Dependence of mean waiting time 〈τw〉 on final liquid temperature T liq for systems of N = 7776 (black circles), 976 (red squares), 392 (green diamonds), 150 (blue triangles) and 96 (brown stars) atoms. Quantity plotted is 〈τw〉−1/2 as function of T liq. Straight lines are linear least-squares fits to the data for each N value.
Scaling of mean waiting times 〈τw〉 with system size specified by number of atoms N. Quantity plotted is (N〈τw〉)−1/2 as function of final liquid temperature T liq.
Alternation between solid and liquid states: temperature as function of time in one of the constant-energy MD simulations on the system of 96 atoms, with total energy such that mean liquid-state temperature is T liq = 6760 K, showing alternation between mean temperatures T sol and T liq.
Histograms of temperature distribution at different constant total energies E in the system of 96 atoms. The histogram at each E was obtained by sampling over typically 128 simulations, each having a typical duration of 5 ns. Instead of giving E directly, we specify each histogram by the liquid-state temperature T liq. Histograms shown by solid (black), dashed (red), dotted (green), chain (blue), and dotted-chain (black) lines are for T liq = 6935, 6760, 6590, 6565, and 6473 K.
Fraction of time spent by the system in the liquid state for different liquid-state temperatures T liq in simulations of 96-atom system.
Z plot from a sequence of constant-energy AIMD simulations on system of 150 atoms, duration of simulations being 50 ps. Black filled circles with error bars show final mean temperature and pressure, with upper-left branch corresponding to energies for which the system remains solid, and lower right branch to energies for which homogeneous melting occurs. Dashed (red) line shows the ab initio melting curve obtained in earlier work using the free energy technique, and green filled square with error bar shows point on ab initio melting curve obtained with ab initio MD simulations on a system of 980 atoms containing coexisting solid and liquid.
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