Dynamics of anharmonic surfaces in harmonic crystals

✍ Scribed by P. Zieliński; Z. Łodziana; T. Srokowski

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 469 KB
• Volume: 59
• Category: Article
• ISSN: 0079-6816
• DOI: 10.1016/s0079-6816(98)00052-5

✦ Synopsis

Explicit expressions are given for the effective equations of motion for surface atoms placed in a general anharmonic potential and attached to semi-infinite harmonic bulk substrates. Three types of one-dimensional substrates are considered: i) continuous dispersionless, ii) discrete with nearest neighbours harmonic interactions, and iii) a substrate showing a strong spatial dispersion due to next-nearest neighbours interactions. The elimination of the harmonic degrees of freedom of the dispersionless substrate i) reduces the problem to the damped Duffing oscillator in the case of an external force applied to the surface atom, and to an extended Duffing oscillator with time-dependent coefficients in the case of scattering of a phonon incoming from the bulk. In both remaining cases [ii) and iii)] the resulting equations of motion are Volterra integrodifferential equations. The equations of motion obtained allow for the study of transitive regimes, of higher harmonics generation and of chaotic behaviour, due to the surface anharmonicity.