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Ab initio calculations are becoming increasingly important for designing new alloys as these calculations can accurately predict basic structural, mechanical, and functional properties using only the atomic composition as a basis. In this paper, fundamental physical properties (like formation energies and elastic constants) of a set of bcc Mg-Li and Mg-Li-based compounds are calculated using density functional theory (DFT). These DFT-determined properties are in turn used to calculate engineering parameters such as (i) specific Young's modulus (gamma/rho) or (ii) shear over bulk modulus ratio (GIB) differentiating between brittle and ductile behavior. These parameters are then used to identify those alloys that have optimal mechanical properties for lightweight structural applications. First, in case of the binary Mg-Li system, an Ashby map containing gamma/rho versus GIB shows that it is not possible to increase gamma/rho without simultaneously increasing GIB (i.e., brittleness) by changing only the composition of a binary alloy. In an attempt to bypass such a fundamental materials-design limitation, a set of Mg-Li-X ternaries (X = Ca, Al, Si, Cu, Zn) based on stoichiometric Mg-Li with CsCl structure was studied. It is shown that none of the studied ternary solutes is able to simultaneously improve both specific Young's modulus and ductility.