Electron-Spin Susceptibilities of the Liquid Binary Alkali Metal Alloys

Abstract

We report measurements of the Knight shifts of the liquid binary alkali metal alloys over the entire range of concentration of constituents for the alloys Na-Cs, K-Rb, K-Cs, and Rb-Cs. We interpret all existing measurements of the Knight shift in the binary alloys of Na, K, Rb, and Cs to give the electron-spin susceptibility ${\ensuremath{\chi}}_{e}$ of those pure alkalis not previously measured. Our interpretation uses the assumption that ${〈{|\ensuremath{\psi}(0)|}^{2}〉}_{{E}_{F}}$ for a particular constituent of a particular alloy remains constant, equal to that for the pure metal, over the entire concentration range in that alloy. In previous work on the alkali alloys, the changes in the Knight shift in dilute alloys were attributed solely to changes in ${〈{|\ensuremath{\psi}|}^{2}〉}_{{E}_{F}}$ due to scattering by impurity atoms, whereas we attribute the changes primarily to changes in ${\ensuremath{\chi}}_{e}$ and the atomic volume. New results for pure metals, in cgs volume units, are ${\ensuremath{\chi}}_{c}=(0.84\ifmmode\pm\else\textpm\fi{}0.08)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for potassium and ${\ensuremath{\chi}}_{e}=(0.80\ifmmode\pm\else\textpm\fi{}0.08)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for both rubidium and cesium. Our values are based upon the measured value ${\ensuremath{\chi}}_{e}=1.13\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for sodium as a calibration point. The inferred susceptibilities are consistent with values of the parameter $\ensuremath{\xi}$ of 0.69\ifmmode\pm\else\textpm\fi{}0.07, 0.72\ifmmode\pm\else\textpm\fi{}0.07, and 0.79\ifmmode\pm\else\textpm\fi{}0.08 for potassium, rubidium, and cesium, respectively, where $\ensuremath{\xi}$ is the ratio of electron wave function density at the nucleus in the metal to the same quantity in the free atom. We compare the inferred susceptibilities with the calculations of Silverstein. We also make comparisons via the measured total susceptibilities for the alkalis with some existing calculations of the diamagnetic and ionic susceptibilities for these metals.