Calculation of dispersion relation and real atomic vibration of fcc crystals containing dopant atom using effective potential

Abstract

A new procedure for calculation and analysis of dispersion relation and real atomic vibration of fcc crystals containing dopant atom has been developed using anharmonic effective potential. Analytical expressions for dispersion relation separated by acoustic and optical branches; forbidden zone; effective force constant; Debye frequency and temperature; amplitude and phase of real vibration of atomic chain containing dopant atom have been derived. They contain Morse potential parameters characterizing vibration of each pair of atoms. Numerical calculations have been carried out for Cu doped by Ni or by Al. The results agree well with fundamental properties of these quantities and with experimental values extracted from measured Morse parameters.