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Zeitschrift für Kristallographie - Crystalline Materials

Ed. by Antipov, Evgeny / Bismayer, Ulrich / Huppertz, Hubert / Petrícek, Václav / Pöttgen, Rainer / Schmahl, Wolfgang / Tiekink, E. R. T. / Zou, Xiaodong

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First-principle studies of the lattice dynamics of crystals, and related properties

Xavier Gonze / Gian-Marco Rignanese / Razvan Caracas

Citation Information: Zeitschrift für Kristallographie. Volume 220, Issue 5/6/2005, Pages 458–472, ISSN (Print) 0044-2968, DOI: 10.1524/zkri.220.5.458.65077, September 2009

Publication History

July 19, 2004
October 13, 2004
Published Online:


The crystal lattice is never rigid. Due to temperature, external fields or pressure, the nuclei vibrate, the lattice distorts, and instabilities can induce phase transitions. We review the basic concepts of density-functional perturbation theory, a computational method especially suited to determine from first-principles the microscopic parameters governing such behaviour. Then, we present the additional formalism leading to the following properties of minerals: the infra-red and Raman spectra; the prediction of (meta)stability or instability of a crystalline phase, based on the phonon spectrum; the computation of thermodynamics quantities like the free energy, entropy, specific heat; the atomic temperature factors. For each property, examples are given. When appropriate, we mention the computation of related properties, like dielectric tensor and Born effective charges that are needed to get infra-red spectra. Finally, we discuss briefly, on one hand, other applications of the density-functional perturbation theory, and, on the other hand, an alternative technique, the finite-difference computation of dynamical matrices.

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