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

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Mermin-Wagner fluctuations in 2D amorphous solids.

Bernd Illing¹, Sebastian Fritschi¹, Herbert Kaiser¹

¹Department of Physics, University of Konstanz, Konstanz 78464, Germany.

Proceedings of the National Academy of Sciences of the United States of America

|February 1, 2017

Summary

This summary is machine-generated.

Mermin-Wagner fluctuations in two-dimensional systems are caused by density fluctuations, not glassy relaxations. These fluctuations allow for large atomic displacements, challenging traditional models of 2D materials.

Keywords:

2D ensembles Mermin–Wagner fluctuations confined geometry glass transition phase transition

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Area of Science:

Condensed Matter Physics
Materials Science
Statistical Mechanics

Background:

The Mermin-Wagner theorem explains the absence of broken continuous symmetries in 2D systems due to long-wavelength fluctuations.
In two dimensions, these fluctuations impact both structure and dynamics, causing the Lindemann criterion for melting to fail.
Previous understanding doubted the existence of 2D crystals and the behavior of materials in two dimensions.

Purpose of the Study:

To differentiate Mermin-Wagner fluctuations from glassy structural relaxations in two-dimensional systems.
To investigate the dynamical impact of Mermin-Wagner fluctuations on atomic displacements.
To explore the role of periodicity in Mermin-Wagner fluctuations.

Main Methods:

Comparison of experimental data from 3D and 2D amorphous solids with 2D crystalline materials.
Utilizing computer simulations to model atomic displacements and system size effects.
Analyzing the Lindemann criterion in the context of two-dimensional systems.

Main Results:

Mermin-Wagner fluctuations were successfully disentangled from glassy relaxations.
Computer simulations demonstrated a logarithmic increase in atomic displacements with system size.
The study confirmed that periodicity is not essential for Mermin-Wagner fluctuations.

Conclusions:

Mermin-Wagner fluctuations are a key factor governing the behavior of two-dimensional materials.
These fluctuations allow for significant atomic displacements, impacting material properties.
The homogeneity of space on long scales is preserved by Mermin-Wagner fluctuations, irrespective of periodicity.