Thermal vacancies in close-packing solids

Mortazavifar, Mostafa; Oettel, Martin

doi:10.1209/0295-5075/105/56005

Cited by 3 publications

(6 citation statements)

References 25 publications

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“…For pure HS, the order of magnitude for the equilibrium vacancy concentration can be estimated by βf eff (min{α G }) -βf eff (min{ρ c (r)}) q = 0.1 η p,r = 0.05 (where p HS is the crystal pressure) [29]. Within DFT descriptions of hard spheres, only FMT, specifically only the WBII(tensor) functional, delivers equilibrium vacancy concentrations of this order of magnitude (both for constrained and full minimization) [16].…”

Section: Equilibrium Vacancy Concentrationsmentioning

confidence: 99%

“…Within DFT descriptions of hard spheres, only FMT, specifically only the WBII(tensor) functional, delivers equilibrium vacancy concentrations of this order of magnitude (both for constrained and full minimization) [16]. For the AO model, the methods of [29] can be used to derive an analytical estimate for n vac,eq which is given by…”

Section: Equilibrium Vacancy Concentrationsmentioning

confidence: 99%

“…In [29], we have derived an expression for the equilibrium vacancy concentration n vac,eq in crystals, based on a cell cluster expansion for the partition function originally suggested in [38]. This cluster expansion for the configurational part of the N-particle partition function Q N for a one-component substance consists in a product series of partition functions Z i l , Z ij l , ... for one, two, ... freely moving particles labelled i, ij, ... in a matrix of N − 1, N − 2, ... particles fixed at ideal lattice sites.…”

Section: Appendix a Vacancy Concentration In Ao Crystalsmentioning

confidence: 99%

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A fundamental measure density functional for fluid and crystal phases of the Asakura–Oosawa model

Mortazavifar

Oettel²

2016

J. Phys.: Condens. Matter

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We investigate a density functional for the Asakura-Oosawa model of colloid-polymer mixtures, describing both fluid and crystal phases. It is derived by linearizing the two-component fundamental-measure hard sphere tensor functional in the second (polymer) component. We discuss the formulation of an effective density functional for colloids only. For small polymer-colloid size ratios the effective, polymer-induced potential between colloids is short-range attractive and of two-body form but we show that the effective density functional is not equivalent to standard mean-field approaches where attractions are taken into account by terms second order in the colloid density. We calculate numerically free energies and phase diagrams in good agreement with available simulations, furthermore we discuss the colloid and polymer distributions in the crystal and determine equilibrium vacancy concentrations. Numerical results reveal a fairly strong sensitivity to the specific type of underlying fundamental measure hard sphere functional which could aid further development of fundamental measure theory.

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Section: Equilibrium Vacancy Concentrationsmentioning

confidence: 99%

Section: Equilibrium Vacancy Concentrationsmentioning

confidence: 99%

Section: Appendix a Vacancy Concentration In Ao Crystalsmentioning

confidence: 99%

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A fundamental measure density functional for fluid and crystal phases of the Asakura–Oosawa model

Mortazavifar

Oettel²

2016

J. Phys.: Condens. Matter

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“…The hard-sphere model system is one of the most extensively investigated systems and has strongly contributed to a basic understanding of a variety of fundamental phenomena in condensed matter physics, such as glass transitions, [5][6][7] crystal nucleation, [8][9][10][11][12][13] and optimal packings. [14][15][16][17] Likewise, hard spheres provide a simple model system to study crystal defects, both in statistical mechanical theories [18][19][20][21] and in experiments using "colloidal" hard spheres. [22][23][24][25][26][27] While these experiments on colloidal particles allow for direct quantitative studies of crystals in real space and real time, studying their defects is typically very challenging.…”

Section: Introductionmentioning

confidence: 99%

Diffusion and interactions of point defects in hard-sphere crystals

Meer

Dijkstra

Filion

2017

The Journal of Chemical Physics

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Using computer simulations, we study the diffusion, interactions, and strain fields of point defects in a face-centered-cubic crystal of hard spheres. We show that the vacancy diffusion decreases rapidly as the density is increased, while the interstitial diffusion exhibits a much weaker density-dependence. Additionally, we predict the free-energy barriers associated with vacancy hopping and find that the increasing height of the free-energy barrier is solely responsible for the slowing down of vacancy diffusion. Moreover, we find that the shape of the barriers is independent of the density. The interactions between vacancies are shown to be weakly attractive and short-ranged, while the interactions between interstitials are found to be strongly attractive and are felt over long distances. As such, we find that vacancies do not form vacancy clusters, while interstitials do form long-lived interstitial clusters. Considering the strain field of vacancies and interstitials, we argue that vacancies will hardly feel each other, as they do not substantially perturb the crystal, and as such exhibit weak interactions. Two interstitials, on the other hand, interact with each other over long distances and start to interact (attractively) when their strain fields start to overlap.

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“…At present, only FMT-type functionals can deliver values for n vac , which are of the correct order of magnitude (∼10 −4 , see Ref. [31] for a theoretical explanation of this order of magnitude). Other functionals (such as Taylor expanded functionals or the PFC model) give |n vac | ∼ O(0.1), with even possibly negative signs (corresponding to a presence of excess interstitials which is unphysical for the hard sphere system) [15].…”

Section: B Functionals Using An Empirical Parametermentioning

confidence: 93%

Fundamental measure theory for the inhomogeneous hard-sphere system based on Santos' consistent free energy

et al. 2015

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Based on Santos' general solution for the scaled-particle differential equation [Phys. Rev. E 86, 040102(R) (2012)], we construct a free-energy functional for the hard-sphere system. The functional is obtained by a suitable generalization and extension of the set of scaled-particle variables using the weighted densities from Rosenfeld's fundamental measure theory for the hard-sphere mixture [Phys. Rev. Lett. 63, 980 (1989)]. While our general result applies to the hard-sphere mixture, we specify remaining degrees of freedom by requiring the functional to comply with known properties of the pure hard-sphere system. Both for mixtures and pure systems, the functional can be systematically extended following the lines of our derivation. We test the resulting functionals regarding their behavior upon dimensional reduction of the fluid as well as their ability to accurately describe the hard-sphere crystal and the liquid-solid transition.

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Thermal vacancies in close-packing solids

Cited by 3 publications

References 25 publications

A fundamental measure density functional for fluid and crystal phases of the Asakura–Oosawa model

A fundamental measure density functional for fluid and crystal phases of the Asakura–Oosawa model

Diffusion and interactions of point defects in hard-sphere crystals

Fundamental measure theory for the inhomogeneous hard-sphere system based on Santos' consistent free energy

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