Effect of the Translational-Diffusion Mechanism on the Low-Field NMR Spin-Lattice Relaxation Time in the Rotating Reference Frame: Calculation of the Order Parameterp

Abstract

The effect of the translational-diffusion mechanism on the low-field NMR spin-lattice relaxation time in the rotating reference frame is calculated for simple cubic, body-centered cubic, and face-centered cubic lattices. The results of these calculations suggest a new method for determining the preferred diffusion mechanism. Previously NMR has been able to provide a direct measurement of the activation energy only; a theory has always been needed to determine the jump frequency from the experimentally measured relaxation time. Recently Slichter and Ailion developed a new technique for the study of ultraslow diffusion which is applicable when the mean time $\ensuremath{\tau}$ between atomic jumps is less than the spin-lattice relaxation time ${T}_{1}$. In their theory, an order parameter $p$ appears in the relationship between the experimentally measured relaxation time and $\ensuremath{\tau}$. This parameter $p$ depends upon the diffusion mechanism and the angle $\ensuremath{\theta}$, which describes the orientation of the crystal with respect to the external magnetic field. In this paper we have calculated $p$ versus $\ensuremath{\theta}$ for vacancy diffusion, interstitialcy diffusion, and interstitial diffusion in bcc, fcc, and sc lattices for two cases. In the first case, we have assumed that ${\ensuremath{\tau}}_{i}$, the mean time that an interstitial atom occupies a particular site between jumps, is longer than ${T}_{2}$, the spin-spin relaxation time, and we have found that the angular dependence of $p$ is quite different for different mechanisms. In the second case, we have assumed that ${\ensuremath{\tau}}_{i}<{T}_{2}$ and have found that the angular dependence of $p$ for interstitialcy diffusion differs from the vacancy results by approximately 10% for the three lattices considered. These theoretical results, when combined with experimental measurements of the angular dependence of the low-field relaxation time, provide a method for the direct determination of the mechanism responsible for diffusion in these crystals.