Elastic properties of Mg(1-x)AlxB2 from first principles theory

• Elastic properties of Mg(1−x)AlxB2 have been studied from first principles. The elastic constants (c11, c12, c13, c33 and c55) have been calculated, in the regime of x = 0 to 0.25. From these calculations the ratio between the bulk modulus and shear modulus (B/G) as well as the ratio between the two directional bulk moduli (Ba/Bc) have been evaluated. Our calculations show that the ratio Ba/Bc decreases monotonically as the aluminium content is increased, whereas the ratio B/G is well below the empirical ductility limit, 1.75, for all concentrations. In addition, we analyse the electronic structure and the nature of the chemical bonding, using the balanced crystal orbital overlap population (BCOOP) (Grechnev et al 2003 J. Phys.: Condens. Matter 15 7751) and the charge densities. Our analysis suggests that, while aluminium doping decreases the elastic anisotropy of MgB2 in the a and c directions, it will not change the brittle behaviour of the material considerably. 

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