Abstract
Using the first-and second-derivatives of the effective interatomic potential in the microscopic electronic theory, the interatomic force constants are calculated for practical material Al with low density and for alkali metal K with high density. The interatomic force constants so obtained are in good agreement with those derived from fitting the experimental phonon spectra and give a set of important data for the binding forces of solids. Dynamical elastic constants are also calculated using the long-wave phonon method and are also compared with observed data from ultrasonic pulse method. The compressibility problem, proposed by Brovman and Kagan, is that the lattice dynamical method in terms of second-order perturbation based on the pseudopotential does not give the self-consistent results for calculation of the elastic constants accompanied by a volume change. This problem is studied quantitatively and is shown to be important for Al and K. Consecluently, the obtained data of the elastic constants C11, C12 and bulk modulus B related to volume change are in good agreement with the observed data in spite of introducing no adjustable parameter. Then, in quasi-harmonic approximation considering temperatureand pressure-dependence of the lattice constant, the temperature and pressure effect on the elastic constants are calculated. The obtained data are consistent with the qualitative tendency of observed data and are useful in studying the mechanical and thermal properties of theses materials.
