Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

1 results

  • 9 - Crystal lattice dynamics, structure, and thermodynamics

  • Mikhail I. Katsnelson, Radboud Universiteit Nijmegen
  • Book:
    The Physics of Graphene
    Published online:
    24 May 2020
    Print publication:
    19 March 2020, pp 213-256

  • Summary

    This chapter mostly explains the role of graphene as a prototype crystalline membrane. We discuss peculiarities of phonon spectra of two-dimensional crystals, such as existence of soft flexural modes and unavoidably decisive role of anharmonic effects, the physical origin of negative thermal expansion of graphene and Mermin–Wagner theorem forbidding long-range crystalline order for two-dimensional materials. We consider mechanics and statistical mechanics of crystalline membranes and especially the role of thermal fluctuations resulting in intrinsic ripples. At the end of this chapter, we give a basic introduction to Raman spectroscopy which is one of the most important experimental tools to probe the properties of graphene.