The second and third order elastic constants of magnesium

Abstract

The complete set of the ten third order elastic constants of magnesium has been determined experimentally from measurements of the hydrostatic pressure and uniaxial compression derivatives of the natural sound velocities using an ultrasonic pulse superposition technique. The specimen was neutron irradiated to suppress dislocation effects. A theoretical model has been developed to predict the elastic constants of magnesium. The energy density of the metal consisted of a volume-dependent term, an electrostatic term, and a band structure term which was derived from pseudopotential theory. The pseudopotential used was the local one proposed by Ashcroft and used by Suzuki, et al. in calculating the elastic constants of cubic metals. The only adjustable parameter was the core radius r . c The calculations were carried out for five different core radii in order to determine the r which gives the best agreement between theory and c experiment. Both the Hartree dielectric function and a modified dielectric function were used; the results were found to be rather insensitive to whichever dielectric function is used. From a comparison of the calculated elastic constants with experiment, it was found that the best agreement was obtained for r = 1.358 a (and the modified dielectric function); there was only a c 0 slight preference, however, over r = 1.38 a (and the Hartree dielectric c 0 function). The core radius determined from elastic constant calculations was found to be in good agreement with the values obtained by other investigators from a comparison of theory with experiment for electronic properties, such as the resistivity of liquid magnesium. Thus the same pseudopotentia1 has proved successful in predicting both mechanical and electronic properties of magnesium. Because magnesium exists in the non-primitive hexagonal close-packed structure, a macroscopic strain gives rise to inter1attice displacements, i.e., internal strains. The internal strain parameter has been calculated by requiring the energy density of the strained state to be a minimum. It was seen that internal strain contributions to the Brugger elastic constants were small; the inclusion of internal strain, however, was found to improve the overall agreement between theory and experiment. The calculated third order elastic constants of magnesium, obtained from using r = 1.358 a and a modified dielectric function, are presented below, along with the experimentally determined values; the elastic constants here are in units of 10 dynes cm Theory Experiment [values]