Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userThe direct correlation function of a crystalline solid
53
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
Direct correlation functions (DCFs), linked to the second functional derivative of the free energy with respect to the one-particle density, play a fundamental role in a statistical mechanics description of matter. This holds in particular for the ordered phases: DCFs contain information about the local structure including defects and encode the thermodynamic properties of crystalline solids; they open a route to the elastic constants beyond low temperature expansions. Via a numerical tour de force we have explicitly calculated for the first time the DCF of a solid: based on the fundamental measure concept we provide results for the DCF of a hard sphere crystal. We demonstrate that this function differs at coexistence significantly from its liquid counterpart - both in shape as well as in its order of magnitude - because it is dominated by vacancies. We provide evidence that the traditional use of liquid DCFs in functional Taylor expansions of the free energy is conceptually wrong and show that the emergent elastic constants are in good agreement with simulation-based results.
rate research
Read More
The identification of the different phases of a two-dimensional (2d) system, which might be in solid, hexatic, or liquid, requires the accurate determination of the correlation function of the translational and of the bond-orientational order parameters. According to the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory, in the solid phase the translational correlation function decays algebraically, as a consequence of the Mermin-Wagner long-wavelength fluctuations. Recent results have however reported an exponential-like decay. By revisiting different definitions of the translational correlation function commonly used in the literature, here we clarify that the observed exponential-like decay in the solid phase results from an inaccurate determination of the symmetry axis of the solid; the expected power-law behaviour is recovered when the symmetry axis is properly identified. We show that, contrary to the common assumption, the symmetry axis of a 2d solid is not fixed by the direction of its global bond-orientational parameter, and introduce an approach allowing to determine the symmetry axis from a real space analysis of the sample.
A solid conducts heat through both transverse and longitudinal acoustic phonons, but a liquid employs only longitudinal vibrations. Here, we report that the crystalline solid AgCrSe2 has liquid-like thermal conduction. In this compound, Ag atoms exhibit a dynamic duality that they are exclusively involved in intense low-lying transverse acoustic phonons while they also undergo local fluctuations inherent in an order-to-disorder transition occurring at 450 K. As a consequence of this extreme disorder-phonon coupling, transverse acoustic phonons become damped as approaching the transition temperature, above which they are not defined anymore because their lifetime is shorter than the relaxation time of local fluctuations. Nevertheless, the damped longitudinal acoustic phonon survives for thermal transport. This microscopic insight might reshape the fundamental idea on thermal transport properties of matter and facilitates the optimization of thermoelectrics.
We report results of direct measurements of velocity profiles in a microchannel with hydrophobic and hydrophilic walls, using a new high precision method of double-focus spacial fluorescence cross-correlation under a confocal microscope. In the vicinity of both walls the measured velocity profiles do not turn to zero by giving a plateau of constant velocity. This apparent slip is proven to be due to a Taylor dispersion, an augmented by shear diffusion of nanotracers in the direction of flow. Comparing the velocity profiles near the hydrophobic and hydrophilic walls for various conditions shows that there is a true slip length due to hydrophobicity. This length, of the order of several tens of nanometers, is independent on electrolyte concentration and shear rate.
The molecular rearrangements of most fluids under flow and deformation do not directly follow the macroscopic strain field. In this work, we describe a phenomenological method for characterizing such non-affine deformation via the anisotropic pair distribution function (PDF). We demonstrate now the microscopic strain can be calculated in both simple shear and uniaxial extension, by perturbation expansion of anisotropic PDF in terms of real spherical harmonics. Our results, given in the real as well as the reciprocal space, can be applied in spectrum analysis of small-angle scattering experiments and non-equilibrium molecular dynamics simulations of soft matter under flow.
New relations among the mixture direct correlation function integrals (or fluctuation integrals) in terms of concentration variables are developed. These relations indicate that, for example, for a binary mixture only one of the three direct correlation function integrals (or one of the three fluctuation integrals is independent. Different closure expressions for mixture cross direct correlation function integrals are suggested and they are joined with the exact relations to calculate all the direct correlation function integrals and fluctuation integrals in a mixture. The results indicate the possibility of introduction of simple closure expressions relating unlike- and like-interaction direct correlation integrals. It is demonstrated that the relation between the direct correlation integrals of hard-sphere mixtures can be satisfactorily represented by a simple geometric mean closure.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
