Structure of large noncrystalline Lennard-Jones models
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Institute of Chemical Kinetics and Combustion, Siberian Division, Russian Academy of Sciences
, Novosibirsk
The structure of computer models (100,000 atoms interacting with the Lennard-Jones potential) is analyzed for liquids and amorphous solids at different temperatures. The structural laws of instantaneous and inherent (I and F) structures are compared. Ample information about structural regularities may be obtained using Delaunay simplices (DS) as structural elements. Various distributions of the properties of the simplices are considered which allow one to determine the prevailing forms of simplices and their transformations at different temperatures. Percolation analysis is used to describe the spatial arrangement of simplices throughout the model.
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octahedron) called good tetrahedron and good quartoctahedron [6-13]. As is known [14], the crystal structure of close
packings of spheres may be represented as a set of perfect tetrahedra and octahedra (that define the configuration of
interatomic voids). Thus the structural elements that prevail in the structure of a liquid (Delaunay simplices) are the same as
those that form the structure of a crystal. In crystal, however, the relative arrangement of these elements is absolutely
different. While crystals always have quartoctahedra united into octahedra, liquids primarily have individual quartoctahedra,
sometimes integrated into semioctahedra, but very seldom into whole octahedra.
The advantage of this choice of structural elements is that their relative positions can be investigated by methods of
percolation theory [15, 16]. The centers of Delaunay simplices (the centers of circumspheres around their vertices) are the
sites of the Voronoi network, which is a set of vertices and edges of a mosaic composed of all Voronoi polyhedra of the
system. Percolation analysis is selecting (coloring) the sites on this network that correspond to simplices with certain
metrical properties (for example, good tetrahedra or quartoctahedra) and considering their relative positions (contiguity).
Importantly, one can proceed with arbitrarily distant simplices since the Voronoi network is defined throughout the model.
While investigation of the properties of the individual Voronoi polyhedra or Delaunay simplices (or of the radial distribution
functions of atoms) provides information about the local structure, percolation analysis allows us to consider the structure of
the model as a whole, i.e., the total structure (the term introduced by P. M. Zorky [17, 18]). As shown in our previous works
[5, 6, 8], the total structure of a simple liquid involves Delaunay simplices (nearly ideal tetrahedra, which are the majority of
all DS) arranged into long branched chains with built-in decahedra rings of five edge-sharing tetrahedra.
The stated structural regularities of simple liquids were obtained on small models of 108 [6-9], 500 [10, 12], and
8000 [11] particles interacting with the Lennard-Jones potential. The purpose of the present work is to confirm and refine
these laws using larger models (100,000 atoms) corresponding to different thermodynamic conditions. Large models have
many advantages. They allow better averaging of statistical noise. The radial distribution functions of these models may be
traced to distances of more than 20 particle diameters after which oscillations die away; this enables correct calculation of the
structure factor. Finally, under certain thermodynamic conditions, the atomic packing becomes nonuniform, acquiring voids
of more than ten atomic diameters; clearly, these situations cannot be investigated with small models. By varying the density
and temperature of model preparation, one can observe interesting effects of structure transformation. Earlier [13] we
investigated the structure of empty space and the motions of test particles in these models.
The models were prepared by the following procedure. For each value of density, a random rarefied packing of
atoms was generated and then compressed by simply scaling the coordinates to achieve the required density. Then the highest
temperature ( * = 0.8) was set in the model, and the system was relaxed in an NVT ensemble by the Monte Carlo method.
The temperature was subsequently lowered by 0.1, and the system relaxed to obtain the next configuration. At each stage,
relaxation was repeated until the average reduction of energy per cycle (one step of the Monte Carlo procedure for each atom)
reached 106 and variation of pressure after 1000 cycles became appreciably smaller than the amplitude of oscillations within
the same time interval. As a result, each stage was from 2000 high-temperature cycles to 100,000 low-temperature cycles.
This article discusses only the properties of models with * = 0.85, while models with other densities are mentioned
simply for the sake of comparison. This density equals the density at the triple point for the Lennard-Jones system: t* =
0.850.01 and t* = 0.680.02 [19]. (...truncated)