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Density Functional Formalism as a Description of the Elastic Behavior of a Hard-Sphere Crystal

Pieprzyk Sławomir, Brańka Arkadiusz C., Heyes David M.

Computational Methods in Science and Technology

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2023

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Vol. 29, No. 1-4

57--64

EN

The density functional method of Jaric and Mohanty [Phys. Rev. B ´ 37, 4441 (1988)] for calculating the elastic moduli of crystalline solids is considered here from the perspective of some new findings. The very slow convergence of the reciprocal-lattice vector summations and presence of the three body term in the method’s computational scheme identified in [J. Chem. Phys. 118, 6594 (2003)] is confirmed and discussed. The sensitivity of the results to the scheme parameters, such as the width of the Gaussian density profiles and the Percus-Yevick approximation used for the direct correlation function is explored. The calculations are for a hard-sphere crystal but most conclusions can be applicable to model crystalline solids in general.

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Free Volume Approximation and Equation of State for the fcc Phase of Polydisperse Hard Spheres

Tretiakov K. V., Wojciechowski K. W.

Computational Methods in Science and Technology

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2013

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Vol. 19, No. 1

59--64

EN

Monte Carlo simulations of the fcc phase of polydisperse hard spheres near close packing are reported. An experimental equation of state (EoS) is determined numerically in the NpT ensemble with variable shape of the periodic box. The close packing volume extrapolated from the obtained data shows a good agreement with earlier experiments performed by other methods. A new theoretical EoS, based on the free volume approximation, is proposed. The modified EoS fits experimental data for polydisperse hard spheres better than the approximation used before

3

Influence of the packing effect on stability and transformation of nanoparticles embedded in random matrices

Hermann H., Elsner A., Gemming T.

Materials Science Poland

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2005

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Vol. 23, No. 2

541--549

EN

The compression of random hard sphere systems does not lead to the formation of iscosahedral short - range order. Instead, icosahedral clusters embedded in a hard sphere system with a medium packing fraction are not stable against densification and they dissolve with an increasing packing fraction. Random homogeneous hard sphere models with equal spheres transform into nanometre scale composites of face-centred cubic nanocrystals embedded in a dense random packed matrix when the mean packing fraction of 0.64 is exceeded.

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Elastic properties of the f.c.c. hard sphere crystal free of defects

Wojciechowski K., Tretiakov K. V.

Computational Methods in Science and Technology

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2002

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Vol. 8, nr 2

84--92

EN

Elastic properties of the f.c.c. phase of hard spheres are determined by Monte Carlo simulations of the box fluctuations in the constant pressure ensemble with variable box shape (NpT). It is shown that the extrapolated data differ by only a f ew percent from those obtained by using systems as small as consisted of N = 108 spheres. The present results are also compared with literature results indicating systematic disagreement with some of them. For this reason, an independent method of direct determination of elastic properties by the free energy differentiation with respect to deformation in the fixed box ensemble (NVT) is also used. Very good agreement is observed for the results of the latter method and the NpT method when they are extrapolated to the infinitely large system limit. Moreover, the results obtained in the present paper fulfill the self-consistency test between the density dependence of the pressure and the bulk modulusmuch better than the literature data mentioned.