Abstract
The elastic properties, including elastic constants, bulk, and shear moduli, and anisotropic index of hexagonal Mg${}_{x}$Ti${}_{1\ensuremath{-}x}$B${}_{2}$ (0 \ensuremath{\leqslant} $x$ \ensuremath{\leqslant} 1) are obtained using a first-principles density-functional-theory method. A difference in chemical bonding occurs between Ti-rich and Mg-rich diborides, leading to significantly different elastic properties: a small elastic anisotropy with relatively large bulk and shear moduli for Ti-rich diborides with $x$ 0.25, and a large elastic anisotropy and relatively small bulk and shear moduli for Mg-rich diborides with $x$ > 0.25. The calculated results reveal a dominant role of the interplanar metal-metal bonds in predicting the extent of shear elastic anisotropy in Mg${}_{x}$Ti${}_{1\ensuremath{-}x}$B${}_{2}$ (0 \ensuremath{\leqslant} $x$ \ensuremath{\leqslant} 1).
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