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Register a new userFrom Sticky-Hard-Sphere to Lennard-Jones-Type Clusters
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A relation $mathcal{M}_{mathrm{SHS}tomathrm{LJ}}$ between the set of non-isomorphic sticky hard sphere clusters $mathcal{M}_mathrm{SHS}$ and the sets of local energy minima $mathcal{M}_{LJ}$ of the $(m,n)$-Lennard-Jones potential $V^mathrm{LJ}_{mn}(r) = frac{varepsilon}{n-m} [ m r^{-n} - n r^{-m} ]$ is established. The number of nonisomorphic stable clusters depends strongly and nontrivially on both $m$ and $n$, and increases exponentially with increasing cluster size $N$ for $N gtrsim 10$. While the map from $mathcal{M}_mathrm{SHS}to mathcal{M}_{mathrm{SHS}tomathrm{LJ}}$ is non-injective and non-surjective, the number of Lennard-Jones structures missing from the map is relatively small for cluster sizes up to $N=13$, and most of the missing structures correspond to energetically unfavourable minima even for fairly low $(m,n)$. Furthermore, even the softest Lennard-Jones potential predicts that the coordination of 13 spheres around a central sphere is problematic (the Gregory-Newton problem). A more realistic extended Lennard-Jones potential chosen from coupled-cluster calculations for a rare gas dimer leads to a substantial increase in the number of nonisomorphic clusters, even though the potential curve is very similar to a (6,12)-Lennard-Jones potential.
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We present a new theoretical framework for modelling the fusion process of Lennard-Jones (LJ) clusters. Starting from the initial tetrahedral cluster configuration, adding new atoms to the system and absorbing its energy at each step, we find cluster growing paths up to the cluster sizes of up to 150 atoms. We demonstrate that in this way all known global minima structures of the LJ-clusters can be found. Our method provides an efficient tool for the calculation and analysis of atomic cluster structure. With its use we justify the magic number sequence for the clusters of noble gas atoms and compare it with experimental observations. We report the striking correspondence of the peaks in the dependence on cluster size of the second derivative of the binding energy per atom calculated for the chain of LJ-clusters based on the icosahedral symmetry with the peaks in the abundance mass spectra experimentally measured for the clusters of noble gas atoms. Our method serves an efficient alternative to the global optimization techniques based on the Monte-Carlo simulations and it can be applied for the solution of a broad variety of problems in which atomic cluster structure is important.
We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for $6leq Nleq12$ hard spheres that are sticky, i.e. they interact only when their surfaces are exactly in contact, we use numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters merge, until at long ranges only one or two clusters are left. We compare clusters obtained by continuation with different potentials and find that for short and medium ranges, up to about 30% of particle diameter, the continued clusters are nearly identical, both within and across families of potentials. For longer ranges the clusters vary significantly, with more variation between families of potentials than within a family. We analyze the mechanisms behind the merge events, and find that most rearrangements occur when a pair of non-bonded particles comes within the range of the potential. An exception occurs for nonharmonic clusters, those that have a zero eigenvalue in their Hessian, which undergo a more global rearrangement.
We report on numerical procedures for, and preliminary results on the search for, tunnelling centres in Lennard-Jones clusters, seen as simple model systems of glasses. Several of the double-well potentials identified are good candidates to give rise to two-level systems. The role of boundary effects, and the application of the semiclassical WKB approximation in multidimensional spaces for the calculation of the ground state splitting are discussed.
The binary Kob-Andersen (KA) Lennard-Jones mixture is the standard model for computational studies of viscous liquids and the glass transition. For very long simulations the viscous KA system crystallizes, however, by phase separating into a pure A particle phase forming an FCC crystal. We present the thermodynamic phase diagram for KA-type mixtures consisting of up to 50% small (B) particles showing, in particular, that the melting temperature of the standard KA system at liquid density $1.2$ is $1.028(3)$ in A particle Lennard-Jones units. At large B particle concentrations the system crystallizes into the CsCl crystal structure. The eutectic corresponding to the FCC and CsCl structures is cut-off in a narrow interval of B particle concentrations around 26% at which the bipyramidal orthorhombic ${rm PuBr_3}$ structure is the thermodynamically stable phase. The melting temperatures variation with B particle concentration at two other pressures, as well as at the constant density $1.2$, is estimated from the simulations at pressure $10.19$ using isomorph theory. Our data demonstrate approximate identity between the melting temperature and the onset temperature below which viscous dynamics appears. Finally, the nature of the solid-liquid interface is briefly discussed.
Electrons released from clusters through strong Xray pulses show broad kinetic-energy spectra, extending from the atomic excess energy down to the threshold, where usually a strong peak appears. These low-energy electrons are normally attributed to evaporation from the nano-plasma formed in the highly-charged clusters. Here, it is shown that also directly emitted photo electrons generate a pronounced spectral feature close to threshold. Furthermore, we give an analytical approximation for the direct photo-electron spectrum.
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