ANHARMONIC EFFECTS IN THE FIBONACCI-CHAIN QUASI-CRYSTALS

Structural and dynamical properties of the anharmonic Fibonacci-chain quasicrystal have been studied using the unsymmetrized self-consistent-field method. Nonlinear integral equations forming the basis of this method are reduced to a set of transcendental or algebraic equations for the moments of one-particle functions. In the lowest orders of anharmonicity, these equations have been solved for an arbitrary one-dimensional model of various atoms interacting with the nearest neighbors. Herewith, the thermal expansion, the variances of the atomic positions, and high-order moments have been expressed in terms of the second, third, and fourth derivatives of the interatomic potentials. Quantum corrections have been calculated as well. The general results have been applied to the system with two kinds of atoms alternating with each other in a Fibonacci sequence. The interatomic distances, thermal expansions, and effective amplitudes of anharmonic atomic vibrations are calculated versus the temperature. The influence of anharmonicity on the thermodynamic functions of the Fibonacci chain is also discussed as well as possible applications to some real solids.