PREDICTION OF LATTICE HEAT CAPACITY AND THERMAL CONDUCTIVITY OF A 1-D FIBONACCI QUASICRYSTAL

Abstract

Fibonacci sequence has been considered as a mono-atomic structural model of one-dimensional quasilattice. The phonon dispersion curves and the vibrational density of states were computed for this model using an-harmonic lattice dynamic calculations. The speed of sound in the 1-D quasicrystal model, found to be 2,546 ????????−1compares poorly with 6,420 ????????−1forAl and provides insight on its poor conductivity. Debye approximation method is used to evaluate the density of state and to subsequently compute the Debye’s  temperature of 241.4 K,Debye frequency of 3.16 x 1013 Hz, lattice heat capacity at constant volumeand Thermal Conductivity Kcat low temperatures 0f 1.330 x 103, 1.098 x103, 5.490x103 Jmol-1K-1 and 0.0850, 0.0710, 0.0085 Wm-1K-1 respectively at TD/10K, 20K and 10K.The value of the Debye frequency is within the range of those of glassy nonconducting materials while the Debye temperature is closer to those of semiconductors or insulators. The numerically calculated values of the heat capacity and conductivity provide further confirmatory insight on the poor conductivity of quasicrystals.