Memory Effect in the Spatial Series Based on Diamond and Graphite Crystals.

Ludmila Grigoreva,Nadezhda Strakhova,Vladimir Kazachenko,Veniamin Grigorev,Alexander Razdolsky

doi:10.3390/molecules25225387

Abstract

To study the relation between the structure of a compound and its properties is one of the fundamental trends in chemistry and materials science. A classic example is the well-known influence of the structures of diamond and graphite on their physicochemical properties, in particular, hardness. However, some other properties of these allotropic modifications of carbon, e.g., fractal properties, are poorly understood. In this work, the spatial series (interatomic distance histograms) calculated using the crystal structures of diamond and graphite are investigated. Hurst exponents H are estimated using detrended fluctuation analysis and power spectral density. The values of H are found to be 0.27–0.32 and 0.37–0.42 for diamond and graphite, respectively. The calculated data suggest that the spatial series have long memory with a negative correlation between the terms of the series; that is, they are antipersistent.

Highlights

One of the areas in modern natural science, which attracts the attention of researchers, is fractal geometry and nonlinear dynamics [1,2,3]
We studied the geometric structures of diamond and graphite crystals
The obtained spatial series were analyzed by detrended fluctuation analysis (DFA) and power spectral density (PSD)

Summary

Introduction

One of the areas in modern natural science, which attracts the attention of researchers, is fractal geometry and nonlinear dynamics [1,2,3]. The objects of inquiry can be time or spatial series formed during experimental observations or theoretical calculations. This approach is applied in areas such as astronomy (sun spots) [4], seismology (Earth crust vibrations) [5], physiology (electroencephalograms) [6], meteorology (weather observation data) [7], econophysics (stock quotation) [8], bioinformatics (protein dynamics) [9], and chemistry (concentration changes) [10].

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Conclusion