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\ifmmode^\circ\else\textdegree\fi{}C. A pulse technique was used. ${T}_{1}$ and ${T}_{2}$ were measured with an accuracy of \ifmmode\pm\else\textpm\fi{}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 ${E}_{D}=1.97\ifmmode\pm\else\textpm\fi{}0.04$ eV and ${D}_{0}=0.11\ifmmode\pm\else\textpm\fi{}0.05$ ${\mathrm{cm}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ for ${\mathrm{Cu}}^{63}$, and ${E}_{D}=2.00\ifmmode\pm\else\textpm\fi{}0.04$ eV and ${D}_{0}=0.15\ifmmode\pm\else\textpm\fi{}0.07$ ${\mathrm{cm}}^{2}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ 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 ${({T}_{1}T)}^{\ensuremath{-}1}$ and $K$ to be temperature-independent. However, an increase of \ensuremath{\sim}10% in ${({T}_{1}T)}^{\ensuremath{-}\frac{1}{2}}$ and $K$ was observed as the temperature was raised from 25\ifmmode^\circ\else\textdegree\fi{}C to the mp. Upon melting, there is a jump of 5.0\ifmmode\pm\else\textpm\fi{}0.5% in ${({T}_{1}T)}^{\ensuremath{-}\frac{1}{2}}$ and $K$. In the liquid phase, $K$ rises moderately, whereas ${({T}_{1}T)}^{\ensuremath{-}\frac{1}{2}}$ shows a steep rise of 5% per 100\ifmmode^\circ\else\textdegree\fi{}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 ${({T}_{1}T)}^{\ensuremath{-}\frac{1}{2}}$ 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 ${({T}_{1}T)}^{\ensuremath{-}\frac{1}{2}}$ upon melting is explained in terms of the removal of the Fermi-surface distortion. No explanation is offered for the rise in ${({T}_{1}T)}^{\ensuremath{-}\frac{1}{2}}$ with temperature in the liquid state.