Calculation of local density of states and lattice specific heat of gold- and silver-based dilute alloy at very low temperature

A theoretical study of the low temperature lattice specific heat of Au0.96Cd0.04 and Ag0.96Al0.04 dilute alloys has been carried out. Lattice Green's function method has been used to calculate the local density of states of substitutional impurity and change in lattice specific heat in these alloys. The condition of resonance and localized modes has also been investigated for possible occurrence of these modes. The calculated results of change in specific heat are compared with the experimental measurements and a good agreement between theory and experiment has been obtained. Although, the calculated results did not show any resonance modes, localized modes above the maximum frequency have been obtained. The change in lattice specific heat as a result of introduction of small fraction of impurities is explained on the basis of obtained localized modes.