Static distortion field induced by an anharmonic standing wave

Abstract

A one-dimensional lattice is considered where the atoms are coupled pairwise through a Fermi-Pasta-Ulam potential. Accordingly the potential does not include any competing forces nor frustration. All standing waves, characterised by their single frequency and wave-length, are worked out as integrable vibrational modes. A forbidden gap shows up for frequencies below the maximum phonon frequency assessed by the harmonic limit of the potential. Furthermore each standing wave gives rise to a static distorted pattern of spatial period equal to the wave-length, resulting from the averaged atomic displacement over one vibrational period. The behaviour of the static distortion field is studied versus a parameter describing the anharmonicity of the potential and the mean interatomic distance. Besides its amplitude turns out to grow with the associated vibrational frequency. The bearing of this work on anharmonicity driven structural changes is briefly discussed.

Key Words:

• anharmonic vibrational modes
• structural phase transitions