The calculation of the elastic shear constants of hexagonal metals using the optimized model potential

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Abstract
The formalism is developed for determining the band-structure contributions to the first- and second-order elastic shear constants of hexagonal close-packed metals in terms of the normalized energy-wavenumber characteristic of the optimized model potential theory. A method of calculating the internal strain or inner displacement contribution to 1/2(c11-c12) is also derived, and the results show that it is significant. Two calculations have been made, one including a correction for exchange and correlation, and the other neglecting it. The fuller version for beryllium and magnesium gives. The results for zinc and cadmium appear disastrous, but detailed analysis shows that this may be rectified by modifying the normalized energy-wavenumber characteristic.