Optimisation of multiple time-step hybrid Monte Carlo Wang–Landau simulations in the isobaric–isothermal ensemble for the determination of phase equilibria

Desgranges, Caroline; Kastl, Erica A.; Aleksandrov, Tsvetan; Delhommelle, Jérôme

doi:10.1080/08927021003762738

Cited by 19 publications

(15 citation statements)

References 45 publications

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“…The qSC-EAM potential has been shown to accurately describe thermodynamic properties of liquid metals, [36][37][38][39][40][41][42][43][44] as well as the boiling points of metals 45 and the vapor-liquid equilibrium properties of Copper. 46,47 In the qSC-EAM potential, the potential energy U of a system containing N atoms is written as the sum of a contribution of two-body term and a contribution of a many-body term…”

Section: Simulation Methodsmentioning

confidence: 99%

“…36 This model was shown to accurately model the properties of liquid metals, [36][37][38][39][40][41][42][43][44] as well as the boiling points of metals 45 and the vapor-liquid equilibrium properties of Cu. 46,47 To determine the vapor-liquid properties, as well as the locus of the Zeno line, we use the recently developed Expanded Wang-Landau simulation method. [48][49][50][51] This method leads to an accurate determination of the grand-canonical partition function of a system, and in turn, to all thermodynamic properties, including the vapor and liquid densities at coexistence and the compressibility factor.…”

Section: Introductionmentioning

confidence: 99%

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Scaling Laws and Critical Properties for fcc and hcp Metals

2016

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The determination of the critical parameters of metals has remained particularly challenging both experimentally, because of the very large temperatures involved, and theoretically, because of the many-body interactions that take place in metals. Moreover, experiments have shown that these systems exhibit an unusually strong asymmetry of their binodal. Recent theoretical work has led to new similarity laws, based on the calculation of the Zeno line and of the underlying Boyle parameters, which provided results for the critical properties of atomic and molecular systems in excellent agreement with experiments. Using the recently developed expanded Wang-Landau (EWL) simulation method, we evaluate the grand-canonical partition function, over a wide range of conditions, for 11 fcc and hcp metals (Ag, Al, Au, Be, Cu, Ir, Ni, Pb, Pd, Pt, and Rh), modeled with a many-body interaction potential. This allows us to calculate the binodal, Zeno line, and Boyle parameters and, in turn, obtain the critical properties for these systems. We also propose two scaling laws for the enthalpy and entropy of vaporization, and identify critical exponents of 0.4 and 1.22 for these two laws, respectively.

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Section: Simulation Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Scaling Laws and Critical Properties for fcc and hcp Metals

2016

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“…The Wang-Landau sampling relies on an iterative evaluation of the biased distribution, [103][104][105][106][107][108][109][110][111][112][113][114][115][116][117][118]…”

Section: A Theoretical Frameworkmentioning

confidence: 99%

Evaluation of the grand-canonical partition function using Expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of Silicon

Desgranges,

Delhommelle

2021

Preprint

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We extend Expanded Wang-Landau (EWL) simulations beyond classical systems and develop the EWL method for systems modeled with a tight-binding Hamiltonian. We then apply the method to determine the partition function and thus all thermodynamic properties, including the Gibbs free energy and entropy, of the fluid phases of Si. We compare the results from quantum many-body (QMB) tight binding models, which explicitly calculate the overlap between the atomic orbitals of neighboring atoms, to those obtained with classical many-body force fields (CMB), which allow to recover the tetrahedral organization in condensed phases of Si through e.g. a repulsive 3-body term that favors the ideal tetrahedral angle. Along the vapor-liquid coexistence, between 3000 K and 6000 K, the densities for the two coexisting phases are found to vary significantly (by 5 orders of magnitude for the vapor and by up to 25 % for the liquid) and to provide a stringent test of the models. Transitions from vapor to liquid are predicted to occur for chemical potentials that are 10 − 15 % higher for CMB models than for QMB models, and a ranking of the force fields is provided by comparing the predictions for the vapor pressure to the experimental data. QMB models also reveal the formation of a gap in the electronic density of states of the coexisting liquid at high temperatures. Subjecting Si to a nanoscopic confinement has a dramatic effect on the phase diagram, with e.g. at 6000 K a decrease in liquid densities by about 50 % for both CMB and QMB models and an increase in vapor densities between 90 % (CMB) and 170% (QMB). The results presented here provide a full picture of the impact of the strategy (CMB or QMB) chosen to model many-body effects on the thermodynamic properties of the fluid phases of Si.

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“…In prior study, we combined the WL sampling scheme with various simulation methods to determine the vapour-liquid equilibria of molecular fluids. For instance, we showed that using WL together with hybrid Monte Carlo simulations leads to accurate predictions of the phase equilibria for the Lennard-Jones fluid [7], metals [10], short linear [7] and branched [11] alkanes, as well as polycyclic aromatic hydrocarbons [12,13]. Unlike with prior methods [1,2], working in the NPT ensemble does not require any insertion/deletion steps during the simulation.…”

Section: Introductionmentioning

confidence: 95%

Wang–Landau configurational bias Monte Carlo simulations: vapour–liquid equilibria of alkenes

Ngale

Desgranges

Delhommelle

2012

Molecular Simulation

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We propose to combine the Wang -Landau (WL) sampling scheme with configurational-bias Monte Carlo (CBMC) simulations to study the phase behaviour of chain molecules. We apply the resulting WL -CBMC method to calculate an estimate for the canonical and isothermal -isobaric partition function for a series of alkene molecules. We assess the accuracy of the proposed method by showing that the phase equilibria and the critical properties of four alkenes (propene, butene, pentene and hexene) determined from the WL -CBMC simulations are in excellent agreement with the experimental data and simulation results from Gibbs ensemble Monte Carlo simulations.

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Optimisation of multiple time-step hybrid Monte Carlo Wang–Landau simulations in the isobaric–isothermal ensemble for the determination of phase equilibria

Cited by 19 publications

References 45 publications

Scaling Laws and Critical Properties for fcc and hcp Metals

Scaling Laws and Critical Properties for fcc and hcp Metals

Evaluation of the grand-canonical partition function using Expanded Wang-Landau simulations. IV. Performance of many-body force fields and tight-binding schemes for the fluid phases of Silicon

Wang–Landau configurational bias Monte Carlo simulations: vapour–liquid equilibria of alkenes

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