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°K and is found to obey the empirical relation for change with temperature, $K=-(2.95\mathrm{}\pm 0.15)\times {10}^{-7\mathrm{}}(T-{300}^{\circ })$. 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 $K\left(V\right)=0.00449\mathrm{}{\left(\frac{V}{V_0}\right)}^{-0.1\mathrm{}\pm 0.1}$ 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°K in gallium and from 233 to 356°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 $\frac{1}{T_1}$ (${\sec }^{-1\mathrm{}}$) for gallium and mercury are most simply expressed as a function of temperature in the range of the measurements: ${\mathrm{Ga}}^{69}$, $3.3T+(800-0.67T)\mathrm{}$; ${\mathrm{Ga}}^{71}$, $5.3T+(320-0.27T)\mathrm{}$; ${\mathrm{Hg}}^{199}$, $63T;{\mathrm{Hg}}^{201}$, $8.9T+(69000-80T)$. (In these expressions, the first term gives the hyperfine part; the term in parentheses gives the quadrupole part.)