Free energies, vacancy concentrations, and density distribution anisotropies in hard-sphere crystals: A combined density functional and simulation study

Oettel, Martin; Görig, S.; Härtel, Andreas; Löwen, Hartmut; Radu, Marc; Schilling, Tanja

doi:10.1103/physreve.82.051404

Cited by 64 publications

(125 citation statements)

References 68 publications

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“…The Onsager approximation is valid at low densities reproducing the second virial coefficient of the bulk fluid equation of state correctly but is expected to break down at higher densities. Unfortunately, unlike for hard-core interactions 58,59 , no alternative approximation working at higher densities is known for soft inverse-power-law potentials 60 . However, we expect the general trends to be captured by the theory but not the details of molecular layering.…”

Section: Density Functional Theorymentioning

confidence: 99%

Soft repulsive mixtures under gravity: Brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking

Kruppa

Neuhaus

Messina

et al. 2012

The Journal of Chemical Physics

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A binary mixture of particles interacting via long-ranged repulsive forces is studied in gravity by computer simulation and theory. The more repulsive A-particles create a depletion zone of less repulsive B-particles around them reminiscent to a bubble. Applying Archimedes' principle effectively to this bubble, an A-particle can be lifted in a fluid background of Bparticles. This "depletion bubble" mechanism explains and predicts a brazil nut effect where the heavier A-particles float on top of the lighter B-particles. It also implies an effective attraction of an A-particle towards a hard container bottom wall which leads to boundary layering of A-particles. Additionally, we have studied a periodic inversion of gravity causing perpetuous mutual penetration of the mixture in a slit geometry. In this nonequilibrium case of time-dependent gravity, the boundary layering persists. Our results are based on computer simulations and density functional theory of a two-dimensional binary mixture of colloidal repulsive dipoles. The predicted effects also occur for other long-ranged repulsive interactions and in three spatial dimensions. They are therefore verifiable in settling experiments on dipolar or charged colloidal mixtures as well as in charged granulates and dusty plasmas.

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Section: Density Functional Theorymentioning

confidence: 99%

Soft repulsive mixtures under gravity: Brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking

Kruppa

Neuhaus

Messina

et al. 2012

The Journal of Chemical Physics

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“…19, we start by fixing the packing fraction η r of the reservoir. In a defect-free two-dimensional solid with hexagonal order there would be N = 2 particles per unit cell.…”

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confidence: 99%

Communication: Fundamental measure theory for hard disks: Fluid and solid

Roth

Mecke

Oettel

2012

The Journal of Chemical Physics

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Two-dimensional hard-particle systems are rather easy to simulate but surprisingly difficult to treat by theory. Despite their importance from both theoretical and experimental points of view, theoretical approaches are usually qualitative or at best semi-quantitative. Here, we present a density functional theory based on the ideas of fundamental measure theory for two-dimensional hard-disk mixtures, which allows for the first time an accurate description of the structure of the dense fluid and the equation of state for the solid phase within the framework of density functional theory. The properties of the solid phase are obtained by freely minimizing the functional.

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“…However, furthermore it was found: Z(i) No free energy minimum for n vac > 0 and (ii) equal free energies for fcc and hcp. In a study combining simulation and free minimization of FMT functionals [18] it was shown that (i)…”

Section: Introductionmentioning

confidence: 99%

Stable and metastable hard-sphere crystals in fundamental measure theory

Yamani

Oettel

2013

Phys. Rev. E

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Using fully minimized fundamental measure functionals, we investigate free energies, vacancy concentrations and density distributions for bcc, fcc and hcp hard-sphere crystals. Results are complemented by an approach due to Stillinger which is based on expanding the crystal partition function in terms of the number n of free particles while the remaining particles are frozen at their ideal lattice positions. The free energies of fcc/hcp and one branch of bcc agree well with Stillinger's approach truncated at n = 2. A second branch of bcc solutions features rather spreadout density distributions around lattice sites and large equilibrium vacancy concentrations and is presumably linked to the shear instability of the bcc phase. Within fundamental measure theory and the Stillinger approach (n = 2), hcp is more stable than fcc by a free energy per particle of about 0.001 k B T . In previous simulation work, the reverse situation has been found which can be rationalized in terms of effects due to a correlated motion of at least 5 particles in the Stillinger picture.

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Free energies, vacancy concentrations, and density distribution anisotropies in hard-sphere crystals: A combined density functional and simulation study

Cited by 64 publications

References 68 publications

Soft repulsive mixtures under gravity: Brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking

Soft repulsive mixtures under gravity: Brazil-nut effect, depletion bubbles, boundary layering, nonequilibrium shaking

Communication: Fundamental measure theory for hard disks: Fluid and solid

Stable and metastable hard-sphere crystals in fundamental measure theory

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