Structure analysis methods for crystalline solids and supercooled liquids

Yu, D.Q.; Chen, Min; Han, Xiaohui

doi:10.1103/physreve.72.051202

Cited by 18 publications

(8 citation statements)

References 28 publications

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“…In condensed matter physics, the Voronoi cell of the lattice point of a crystal is known as the Wigner-Seitz cell, whereas the Voronoi cell of the reciprocal lattice point is the Brillouin zone [15,16]. Voronoi tessellations have been used for performing structure analysis for crystalline solids and supercooled liquids [17,18], for detecting glass transitions [19], for emphasizing the geometrical effects underlying the vibrations in the glass [20], and for performing detailed and efficient electronic calculations [21,22] Moreover, a connection has been recently established between the Rayleigh-Bènard convective cells and Voronoi cells, with the hot spots (locations featuring the strongest upward motion of hot fluid) of the former basically coinciding with the points generating the Voronoi cells, and the locations of downward motion of cooled fluid coinciding with the sides of the Voronoi cells [23]. Finally, Voronoi tessellations are a formidable tool for performing arbitrary space integration of sparse data, without adopting the typical procedure of adding spurious information, as in the case of linear or splines interpolations.…”

Section: Introductionmentioning

confidence: 99%

Symmetry-Break in Voronoi Tessellations

Lucarini

2009

Symmetry

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Abstract:We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the OPEN ACCESSSymmetry 2009, 1 22 perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomal...

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Section: Introductionmentioning

confidence: 99%

Symmetry-Break in Voronoi Tessellations

Lucarini

2009

Symmetry

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“…In the past, the cluster results depend on the value of r c [26,42], resulting in an uncertainty in structural quantification. This deficiency can be overcome by finding a natural and unique upper limit of r c , described as follows.…”

Section: Analysis Methodsmentioning

confidence: 98%

Structural evolution in the crystallization of rapid cooling silver melt

Tian

Dong

2015

Annals of Physics

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“…This behavior originates from fluctuations which cause the Voronoi cell of next-nearest neighbors to occasionally share a small face [6]. There exist extensions to the Voronoi construction which attempt to increase the robustness of the algorithm to fluctuations [8][9][10]. However, many of them introduce non-inherent parameters and, as such, are not parameter-free.…”

Section: Bulk Phasesmentioning

confidence: 99%

“…In a crystal, thermal fluctuations which cause particles to fluctuate around their equilibrium lattice sites can spuriously increase the number of particles which share a small face with the target particle [5,6] and hence increase the number of particles identified as nearest neighbors. There exist extensions to the Voronoi construction which aim to increase the robustness against these fluctuations [5,[7][8][9][10], however, they typically introduce parameters, removing the "parameter free" advantage of the algorithm, and they further increase the computational cost.…”

Section: Introductionmentioning

confidence: 99%

A parameter-free, solid-angle based, nearest-neighbor algorithm

Meel

Filion

Valeriani

et al. 2012

The Journal of Chemical Physics

100

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We propose a parameter-free algorithm for the identification of nearest neighbors. The algorithm is very easy to use and has a number of advantages over existing algorithms to identify nearestneighbors. This solid-angle based nearest-neighbor algorithm (SANN) attributes to each possible neighbor a solid angle and determines the cutoff radius by the requirement that the sum of the solid angles is 4π. The algorithm can be used to analyze 3D images, both from experiments as well as theory, and as the algorithm has a low computational cost, it can also be used "on the fly" in simulations. In this paper, we describe the SANN algorithm, discuss its properties, and compare it to both a fixed-distance cutoff algorithm and to a Voronoi construction by analyzing its behavior in bulk phases of systems of carbon atoms, Lennard-Jones particles and hard spheres as well as in Lennard-Jones systems with liquid-crystal and liquid-vapor interfaces.

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Structure analysis methods for crystalline solids and supercooled liquids

Cited by 18 publications

References 28 publications

Symmetry-Break in Voronoi Tessellations

Symmetry-Break in Voronoi Tessellations

Structural evolution in the crystallization of rapid cooling silver melt

A parameter-free, solid-angle based, nearest-neighbor algorithm

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