430 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
Free energy surface of ST2 water near the liquid-liquid phase transition
We carry out umbrella sampling Monte Carlo simulations to evaluate the free
energy surface of the ST2 model of water as a function two order parameters,
the density and a bond-orientational order parameter. We approximate the
long-range electrostatic interactions of the ST2 model using the reaction-field
method. We focus on state points in the vicinity of the liquid-liquid critical
point proposed for this model in earlier work. At temperatures below the
predicted critical temperature we find two basins in the free energy surface,
both of which have liquid-like bond orientational order, but differing in
density. The pressure and temperature dependence of the shape of the free
energy surface is consistent with the assignment of these two basins to the
distinct low density and high density liquid phases previously predicted to
occur in ST2 water.Comment: 8 pages, 9 figure
Crystal Nucleation in a Supercooled Liquid with Glassy Dynamics
In simulations of supercooled, high-density liquid silica we study a range of
temperature T in which we find both crystal nucleation, as well as the
characteristic dynamics of a glass forming liquid, including a breakdown of the
Stokes-Einstein relation. We find that the liquid cannot be observed below a
homogeneous nucleation limit (HNL) at which the liquid crystallizes faster than
it can equilibrate. We show that the HNL would occur at lower T, and perhaps
not at all, if the Stokes-Einstein relation were obeyed, and hence that glassy
dynamics plays a central role in setting a crystallization limit on the liquid
state in this case. We also explore the relation of the HNL to the Kauzmann
temperature, and test for spinodal-like effects near the HNL.Comment: 4 pages, 4 figure
Density minimum and liquid-liquid phase transition
We present a high-resolution computer simulation study of the equation of
state of ST2 water, evaluating the liquid-state properties at 2718 state
points, and precisely locating the liquid-liquid critical point (LLCP)
occurring in this model. We are thereby able to reveal the interconnected set
of density anomalies, spinodal instabilities and response function extrema that
occur in the vicinity of a LLCP for the case of a realistic, off-lattice model
of a liquid with local tetrahedral order. In particular, we unambiguously
identify a density minimum in the liquid state, define its relationship to
other anomalies, and show that it arises due to the approach of the liquid
structure to a defect-free random tetrahedral network of hydrogen bonds.Comment: 5 pages, 4 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
Stochastic Model and Equivalent Ferromagnetic Spin Chain with Alternation
We investigate a non-equilibrium reaction-diffusion model and equivalent
ferromagnetic spin 1/2 XY spin chain with alternating coupling constant. The
exact energy spectrum and the n-point hole correlations are considered with the
help of the Jordan-Wigner fermionization and the inter-particle distribution
function method. Although the Hamiltonian has no explicit translational
symmetry, the translational invariance is recovered after long time due to the
diffusion. We see the scaling relations for the concentration and the two-point
function in finite size analysis.Comment: 7 pages, LaTeX file, to appear in J. Phys. A: Math. and Ge
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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