508 research outputs found
Phase diagram of silica from computer simulation
We evaluate the phase diagram of the ``BKS'' potential [Van Beest, Kramer and
van Santen, Phys. Rev. Lett. 64, 1955 (1990)], a model of silica widely used in
molecular dynamics (MD) simulations. We conduct MD simulations of the liquid,
and three crystals (beta-quartz, coesite and stishovite) over wide ranges of
temperature and density, and evaluate the total Gibbs free energy of each
phase. The phase boundaries are determined by the intersection of these free
energy surfaces. Not unexpectedly for a classical pair potential, our results
reveal quantitative discrepancies between the locations of the BKS and real
silica phase boundaries. At the same time, we find that the topology of the
real phase diagram is reproduced, confirming that the BKS model provides a
satisfactory qualitative description of a silica-like material. We also compare
the phase boundaries with the locations of liquid-state thermodynamic anomalies
identified in previous studies of the BKS model.Comment: 7 pages, 7 figure
Phase diagram of a two-dimensional system with anomalous liquid properties
Using Monte Carlo simulation techniques, we calculate the phase diagram for a
square shoulder-square well potential in two dimensions that has been
previously shown to exhibit liquid anomalies consistent with a metastable
liquid-liquid critical point. We consider the liquid, gas and five crystal
phases, and find that all the melting lines are first order, despite a small
range of metastability. One melting line exhibits a temperature maximum, as
well as a pressure maximum that implies inverse melting over a small range in
pressure.Comment: 11 pages, 13 figure
"Swarm relaxation": Equilibrating a large ensemble of computer simulations
It is common practice in molecular dynamics and Monte Carlo computer
simulations to run multiple, separately-initialized simulations in order to
improve the sampling of independent microstates. Here we examine the utility of
an extreme case of this strategy, in which we run a large ensemble of
independent simulations (a "swarm"), each of which is relaxed to equilibrium.
We show that if is of order , we can monitor the swarm's relaxation
to equilibrium, and confirm its attainment, within , where
is the equilibrium relaxation time. As soon as a swarm of this size
attains equilibrium, the ensemble of final microstates from each run is
sufficient for the evaluation of most equilibrium properties without further
sampling. This approach dramatically reduces the wall-clock time required,
compared to a single long simulation, by a factor of several hundred, at the
cost of an increase in the total computational effort by a small factor. It is
also well-suited to modern computing systems having thousands of processors,
and is a viable strategy for simulation studies that need to produce
high-precision results in a minimum of wall-clock time. We present results
obtained by applying this approach to several test cases.Comment: 12 pages. To appear in Eur. Phy. J. E, 201
A Family of Tunable Spherically-Symmetric Potentials that Span the Range from Hard Spheres to Water-like Behavior
We investigate the equation of state, diffusion coefficient, and structural
order of a family of spherically-symmetric potentials consisting of a hard core
and a linear repulsive ramp. This generic potential has two characteristic
length scales: the hard and soft core diameters. The family of potentials is
generated by varying their ratio, . We find negative thermal expansion
(thermodynamic anomaly) and an increase of the diffusion coefficient upon
isothermal compression (dynamic anomaly) for . As in water,
the regions where these anomalies occur are nested domes in the () or
() planes, with the thermodynamic anomaly dome contained entirely within
the dynamic anomaly dome. We calculate translational and orientational order
parameters ( and ), and project equilibrium state points onto the () plane, or order map. The order map evolves from water-like behavior to
hard-sphere-like behavior upon varying between 4/7 and 6/7. Thus, we
traverse the range of liquid behavior encompassed by hard spheres ()
and water-like () with a family of tunable
spherically-symmetric potentials by simply varying the ratio of hard to
soft-core diameters. Although dynamic and thermodynamic anomalies occur almost
across the entire range , water-like structural anomalies
(i.e., decrease in both and upon compression and strictly correlated
and in the anomalous region) occur only around .
Water-like anomalies in structure, dynamics and thermodynamics arise solely due
to the existence of two length scales, orientation-dependent interactions being
absent by design.Comment: total 21 pages, 6 figure
Distributions of inherent structure energies during aging
We perform extensive simulations of a binary mixture Lennard-Jones system
subjected to a temperature jump in order to study the time evolution of
fluctuations during aging. Analyzing data from 1500 different aging
realizations, we calculate distributions of inherent structure energies for
different aging times and contrast them with equilibrium. We find that the
distributions initially become narrower and then widen as the system
equilibrates. For deep quenches, fluctuations in the glassy system differ
significantly from those observed in equilibrium. Simulation results are
partially captured by theoretical predictions only when the final temperature
is higher than the mode coupling temperature.Comment: 5 pages, 4 figure
Test of classical nucleation theory on deeply supercooled high-pressure simulated silica
We test classical nucleation theory (CNT) in the case of simulations of
deeply supercooled, high density liquid silica, as modelled by the BKS
potential. We find that at density ~g/cm, spontaneous nucleation
of crystalline stishovite occurs in conventional molecular dynamics simulations
at temperature T=3000 K, and we evaluate the nucleation rate J directly at this
T via "brute force" sampling of nucleation events. We then use parallel,
constrained Monte Carlo simulations to evaluate , the free energy
to form a crystalline embryo containing n silicon atoms, at T=3000, 3100, 3200
and 3300 K. We find that the prediction of CNT for the n-dependence of fits reasonably well to the data at all T studied, and at 3300 K yields a
chemical potential difference between liquid and stishovite that matches
independent calculation. We find that , the size of the critical nucleus,
is approximately 10 silicon atoms at T=3300 K. At 3000 K, decreases to
approximately 3, and at such small sizes methodological challenges arise in the
evaluation of when using standard techniques; indeed even the
thermodynamic stability of the supercooled liquid comes into question under
these conditions. We therefore present a modified approach that permits an
estimation of at 3000 K. Finally, we directly evaluate at T=3000
K the kinetic prefactors in the CNT expression for J, and find physically
reasonable values; e.g. the diffusion length that Si atoms must travel in order
to move from the liquid to the crystal embryo is approximately 0.2 nm. We are
thereby able to compare the results for J at 3000 K obtained both directly and
based on CNT, and find that they agree within an order of magnitude.Comment: corrected calculation, new figure, accepted in JC
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