NMR Study of Self-Diffusion and the Electronic Structure of Metallic Copper in the Solid and Liquid States

Abstract

The Knight shift $K$ and the nuclear relaxation times $T_1$ and $T_2$ of Cu in metallic copper have been measured in the temperature range from room temperature up to the metal melting point, and into the liquid state up to 1200°C. A pulse technique was used. $T_1$ and $T_2$ were measured with an accuracy of ±3%, using a spin echo method. $T_2$ becomes equal to $T_1$ at high temperatures. From the data of $T_2$ versus temperature, the diffusion constants for the Cu self-diffusion were calculated using the Eisenstadt-Redfield approach. The values of these constants are $E_D=1.97\mathrm{}\pm 0.04$ eV and $D_0=0.11\mathrm{}\pm 0.05$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ for ${\mathrm{Cu}}^{63}$, and $E_D=2.00\mathrm{}\pm 0.04$ eV and $D_0=0.15\mathrm{}\pm 0.07$ ${\mathrm{cm}}^2$ ${\sec }^{-1\mathrm{}}$ for ${\mathrm{Cu}}^{65}$. The electronic structure of Cu was deduced from the effect of lattice expansion on $K$ and $T_1$. Assuming a free-electron model, one expects both ${\left(T_{1}T\right)}^{-1\mathrm{}}$ and $K$ to be temperature-independent. However, an increase of ∼10% in ${\left(T_{1}T\right)}^{-\frac{1}{2}}$ and $K$ was observed as the temperature was raised from 25°C to the mp. Upon melting, there is a jump of 5.0±0.5% in ${\left(T_{1}T\right)}^{-\frac{1}{2}}$ and $K$. In the liquid phase, $K$ rises moderately, whereas ${\left(T_{1}T\right)}^{-\frac{1}{2}}$ shows a steep rise of 5% per 100°C. This behavior is identical for both isotopes. It is shown that the main mechanism for the nuclear relaxation is the interaction with the conduction electrons. As the ${\left(T_{1}T\right)}^{-\frac{1}{2}}$ and the $K$ temperature dependence cannot be explained by the free-electron model, we relate the behavior to the well-known band structure, using recent measurements and calculations which give the dependence of the density of states on the lattice constants. The jump in ${\left(T_{1}T\right)}^{-\frac{1}{2}}$ upon melting is explained in terms of the removal of the Fermi-surface distortion. No explanation is offered for the rise in ${\left(T_{1}T\right)}^{-\frac{1}{2}}$ with temperature in the liquid state.