2.1 Phonons

Physical properties of crystals

Second Online Edition (2013)

Part 2. Symmetry aspects of excitations

  1. G. Eckold

Published Online: 19 DEC 2013

DOI: 10.1107/97809553602060000911

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Eckold, G. 2013. Phonons. International Tables for Crystallography. D:2:2.1:286–313.

Author Information

  1. Institut für Physikalische Chemie, Universität Göttingen, Tammannstrasse 6, D-37077 Göttingen, Germany

Publication History

  1. Published Online: 19 DEC 2013



This chapter is devoted to the implications of lattice symmetry on the form, i.e. on the eigenvectors, of lattice vibrations. It is restricted to the consideration of perfect crystals and harmonic vibrations. In addition, some aspects of anharmonicity are discussed in terms of a quasi‐harmonic model, yielding the connection between microscopic dynamics and macroscopic thermodynamic quantities such as thermal expansion. In Section 2.1.2, the fundamentals of lattice dynamics are presented, with special emphasis on the role of the dynamical matrix. Section 2.1.3 deals with the symmetry properties of this matrix along with its eigenvectors and eigenfrequencies.


  • Debye model;
  • Debye temperature;
  • Grüneisen parameter;
  • Hamiltonian;
  • Raman spectroscopy;
  • acoustic branches;
  • acoustic modes;
  • anharmonicity;
  • compatibility relations;
  • compressibility;
  • degeneracy;
  • dispersion curves;
  • dynamical matrix;
  • force constants;
  • harmonic approximation;
  • heat capacity;
  • irreducible representations;
  • lattice dynamics;
  • normal coordinates;
  • phonon dispersion;
  • phonons;
  • selection rules;
  • thermal expansion;
  • time‐reversal degeneracy