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Related Experiment Video

Updated: Nov 29, 2025

Gradient Echo Quantum Memory in Warm Atomic Vapor

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

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

Ludmila Grigoreva¹, Alexander Razdolsky², Vladimir Kazachenko²

¹Faculty of Fundamental Physical and Chemical Engineering, Lomonosov Moscow State University, Leninskiye Gory 1/51, 119991 Moscow, Russia.

Molecules (Basel, Switzerland)

|November 21, 2020

Summary

This study reveals fractal properties of diamond and graphite using Hurst exponents. Diamond and graphite exhibit antipersistent spatial series, indicating a negative correlation in their atomic structures.

Keywords:

Hurst exponent diamond graphite long memory

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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses

Published on: June 7, 2018

Area of Science:

Materials Science
Chemistry
Condensed Matter Physics

Background:

The relationship between a compound's structure and its properties is fundamental.
While the influence of diamond and graphite structures on hardness is known, their fractal properties remain less understood.
Investigating fractal properties offers new insights into allotropic carbon modifications.

Purpose of the Study:

To analyze the fractal properties of diamond and graphite crystal structures.
To quantify the antipersistence and long-memory characteristics of their spatial series.
To establish a link between atomic structure and fractal behavior in carbon allotropes.

Main Methods:

Calculation of spatial series (interatomic distance histograms) from crystal structures.
Estimation of Hurst exponents (H) using detrended fluctuation analysis (DFA).
Power spectral density (PSD) analysis to further characterize the series.

Main Results:

Hurst exponents for diamond were found to be in the range of 0.27-0.32.
Hurst exponents for graphite were found to be in the range of 0.37-0.42.
Both diamond and graphite spatial series exhibit antipersistence (H < 0.5), indicating long memory with negative correlation.

Conclusions:

The spatial series of diamond and graphite are antipersistent, suggesting a negative correlation between successive terms.
These findings highlight the complex fractal nature of carbon allotropes beyond their well-known mechanical properties.
The study provides a quantitative method for assessing fractal characteristics in crystalline materials.