Elastic Constants of Magnesium-Lithium Alloys

Abstract

The elastic constants of single crystals of magnesium and of dilute alloys of magnesium with lithium have been measured at 298\ifmmode^\circ\else\textdegree\fi{}K using the pulse-echo technique. The alloys covered the range of 1.841-2.0 electrons per atom. All fundamental elastic constants decrease with increasing lithium content. In terms of $C_{0}^{\ensuremath{-}1}(\frac{\mathrm{dC}}{\mathrm{dx}})$ the values are ${c}_{44}$, (-0.411); $\frac{1}{2}({c}_{11}\ensuremath{-}{c}_{12})$, (-0.235); ${c}_{11}+{c}_{12}+2{c}_{33}\ensuremath{-}4{c}_{13}$, (-0.400) per atom fraction of lithium. These values are corrected for the change in lattice parameter upon alloying by using experimental data on the pressure derivatives of the elastic constants of pure magnesium. The remaining effect is due to alloying alone (change in the electron-atom ratio) and is still negative for all three shear constants. In terms of $C_{0}^{\ensuremath{-}1}{(\frac{\ensuremath{\partial}C}{\ensuremath{\partial}x})}_{v,\frac{c}{a}}$ the values are ${c}_{44}$, (-0.827); $\frac{1}{2}({c}_{11}\ensuremath{-}{c}_{12})$, (-0.589); ${c}_{11}+{c}_{12}+2{c}_{33}\ensuremath{-}4{c}_{13}$, (-0.886) per atom fraction of lithium. These results may be interpreted as indicating, first, a decrease in the long-range electrostatic forces because of the decrease in the average ion-core charge, and second, a decrease in the Fermi stiffness. The decrease in the Fermi stiffness is attributed to: (1) an increase in the volume of electron holes---a hole contributes negatively to the Fermi stiffness---and a decrease in the volume of the overlap electrons in the Brillouin-zone structure with decreasing electron-atom ratio; (2) the transfer (under shear) of electrons from those faces receding from the origin of the Brillouin zone to those approaching it. The over-all effect of this transfer phenomenon is also to decrease the Fermi stiffness.