Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLarge difference in the elastic properties of fcc and hcp hard-sphere crystals
388
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We report a numerical calculation of the elastic constants of the fcc and hcp crystal phases of monodisperse hard-sphere colloids. Surprisingly, some of these elastic constants are very different (up to 20%), even though the free energy, pressure and bulk compressibility of the two crystal structures are very nearly equal. As a consequence, a moderate deformation of a hard-sphere crystal may make the hcp phase more stable than the fcc phase. This finding has implications for the design of patterned templates to grow colloidal hcp crystals. We also find that, below close packing, there is a small, but significant, difference between the distances between hexagonal layers (c/a ratios) of fcc and hcp crystals.
rate research
Read More
We report numerical calculations of the concentration of interstitials in hard-sphere crystals. We find that, in a three-dimensional fcc hard-sphere crystal at the melting point, the concentration of interstitials is 2 * 10^-8. This is some three orders of magnitude lower than the concentration of vacancies. A simple, analytical estimate yields a value that is in fair agreement with the numerical results.
By extending the nonequilibrium potential refinement algorithm and lattice switch method to the semigrand ensemble, the semigrand potentials of the fcc and hcp structures of polydisperse hard-sphere crystals are calculated with the bias sampling scheme. The result shows that the fcc structure is more stable than the hcp structure for polydisperse hard-sphere crystals below the terminal polydispersity.
An approach to obtain the structural properties of additive binary hard-sphere mixtures is presented. Such an approach, which is a nontrivial generalization of the one recently used for monocomponent hard-sphere fluids [S. Pieprzyk, A. C. Branka, and D. M. Heyes, Phys. Rev. E 95, 062104 (2017)], combines accurate molecular-dynamics simulation data, the pole structure representation of the total correlation functions, and the Ornstein-Zernike equation. A comparison of the direct correlation functions obtained with the present scheme with those derived from theoretical results stemming from the Percus-Yevick (PY) closure and the so-called rational-function approximation (RFA) is performed. The density dependence of the leading poles of the Fourier transforms of the total correlation functions and the decay of the pair correlation functions of the mixtures are also addressed and compared to the predictions of the two theoretical approximations. A very good overall agreement between the results of the present scheme and those of the RFA is found, thus suggesting that the latter (which is an improvement over the PY approximation) can safely be used to predict reasonably well the long-range behavior, including the structural crossover, of the correlation functions of additive binary hard-sphere mixtures.
Numerical solutions of the mode-coupling theory (MCT) equations for a hard-sphere fluid confined between two parallel hard walls are elaborated. The governing equations feature multiple parallel relaxation channels which significantly complicate their numerical integration. We investigate the intermediate scattering functions and the susceptibility spectra close to structural arrest and compare to an asymptotic analysis of the MCT equations. We corroborate that the data converge in the $beta$-scaling regime to two asymptotic power laws, viz. the critical decay and the von Schweidler law. The numerical results reveal a non-monotonic dependence of the power-law exponents on the slab width and a non-trivial kink in the low-frequency susceptibility spectra. We also find qualitative agreement of these theoretical results to event-driven molecular-dynamics simulations of polydisperse hard-sphere system. In particular, the non-trivial dependence of the dynamical properties on the slab width is well reproduced.
Descriptors that characterize the geometry and topology of the pore space of porous media are intimately linked to their transport properties. We quantify such descriptors, including pore-size functions and the critical pore radius $delta_c$, for four different models: maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, and inherent structures of the quantizer energy. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. Often, $delta_c$ is used as the key characteristic length scale that determines the fluid permeability $k$. A recent study [Torquato. Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of $k$ based on the second moment of the pore size $langledelta^2rangle$. Here, we confirm that, for all porosities and all models considered, $delta_c^2$ is to a good approximation proportional to $langledelta^2rangle$. However, unlike $langledelta^2rangle$, the permeability estimate based on $delta_c^2$ does not predict the correct ranking of $k$ for our models. Thus, we confirm $langledelta^2rangle$ to be a promising candidate for convenient and reliable estimates of $k$ for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the $tau$ order metric. We find that (effectively) hyperuniform models tend to have lower values of $k$ than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targeted pore statistics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
