Structure Study of Liquid Gallium and Mercury by Nuclear Magnetic Resonance

Abstract

The Knight shift in pure liquid gallium is measured as a function of temperature between 300 and 740\ifmmode^\circ\else\textdegree\fi{}K and is found to obey the empirical relation for change with temperature, $K=\ensuremath{-}(2.95\ifmmode\pm\else\textpm\fi{}0.15)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}7}(T\ensuremath{-}{300}^{\ensuremath{\circ}})$. These data agree with and extend the earlier measurements of McGarvey and Gutowsky, who interpreted their results as being in qualitative agreement with free-electron theory. In the present work the shift is found to vary only slightly with volume, according to the expression $K(V)=0.00449{(\frac{V}{{V}_{0}})}^{\ensuremath{-}0.1\ifmmode\pm\else\textpm\fi{}0.1}$ at pressures between 1 and 5000 kg/${\mathrm{cm}}^{2}$. The nuclear relaxation times ${T}_{1}$ and ${T}_{2}$ are measured from 270 to 470\ifmmode^\circ\else\textdegree\fi{}K in gallium and from 233 to 356\ifmmode^\circ\else\textdegree\fi{}K in mercury. The relaxation rate $\frac{1}{{T}_{1}}$ is divisible into a magnetic hyperfine part and a quadrupolar part. The magnetic part is consistent with the Korringa---Pines theory. The quadrupolar part is explained according to the theory of relaxation by atomic diffusion; good estimates are obtained by using correlation times equal to jump diffusion times reduced by a vacancy fraction of about 0.1 and quadrupole coupling calculated using a single void space at a neighbor position on a quasilattice. The quadrupolar coupling increases with temperature, if the correlation time for the interaction is assumed to be governed by diffusion processes. The experimental relaxation rates $\frac{1}{{T}_{1}}$ (${\mathrm{sec}}^{\ensuremath{-}1}$) for gallium and mercury are most simply expressed as a function of temperature in the range of the measurements: ${\mathrm{Ga}}^{69}$, $3.3T+(800\ensuremath{-}0.67T)$; ${\mathrm{Ga}}^{71}$, $5.3T+(320\ensuremath{-}0.27T)$; ${\mathrm{Hg}}^{199}$, $63T;{\mathrm{Hg}}^{201}$, $8.9T+(69000\ensuremath{-}80T)$. (In these expressions, the first term gives the hyperfine part; the term in parentheses gives the quadrupole part.)