Impurity Diffusion by NMR
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535 IIIPURITY DIFFUSION BY NMR*
JA:1ES R. BECKETT, JEAN POURQUIE and DAVID C. AILION Department of Physics, University of Utah, Salt Lake City, Utah 84112
ABSTRIACT We discuss a recently developed technique for studying the diffusion of spins with a small gyromagnetic ratio and apply it to investigate the nature of Ag+ diffusion in AgF. We also investigate the potential application of this technique to the observation of diffusing impurities. Experimental studies on Cu:3% Al and (P 2 0 5 ) 0 . 8 ([i 2 O) 0 .2 glass are described.
I3TRODUCTiON Nuclear magnetic resonance (0•1R) has long been an important technique for studying the motion of atoms in solids. Since the sensitivity of the NHR signal is proportional both to the gyromagnetic ratio y and to the number of spins of a given species [i1, most NTMRdiffusion studies have been performed on abundant, strongly magnetic (i.e., large y) spin systems rather than on systems which are either weakly magnetic (small y) or in low abundance (impurities). Recently, Stokes and Ailion [2] developed a technique for studying the diffusion of abundant but weakly nagnetic spins (S-spins) whose gyromagnetic ratio may be too small for direct diffusion observations by NMR. In this paper, we shall discuss the application of this technique to two cases in which the diffusing atom is of low abundance: 1) interstitial diffusion and 2) impurity diffusion. DIPOLAR RELAXAT [ON in order to understand the underlying principles of the Stokes-Ailion technique, consider first a diatomic salt consisting of two spin species, one of d;lich Is strongly magnetic (the I spins) and the other is weakly magnetic (the S spins). Suppose, for the moment, that the I spins are diffusing and that the S spins are stationary. One way [31 to observe this diffusion would be to cool the entire dipolar spin system (e.g., by adiabatic demagnetization in the rotating frame) [4] so that each spin is aligned preferentially parallel to the local dipolar field due to its neighbors. A diffusion jump would then cause a local heating of the dipolar system, since the local field at the final site will in general have a different orientation than that at the original site, with the result that the spin orientation will no longer be preferentially parallel to the local field. This local heating will then be transferred to the entire dipolar system by a series of energy conserving spin-flips between neighboring spins. This process of equilibration of dipolar temperature among all the spins is called spin diffusion [51 and occurs at a rate of _ 104 s-1. If the process of spin diffusion is rapid compared to the atomic jumping, then this dipolar relaxation time TID will be of order of the average time Tc between diffusion jumps of each atom. (Actually, one can show [3] that a plot of TID vs. temperature will result in TID having a minimum value at the temperature for which WDTc - L,where AwD is the average dipolar interaction strength experienced by the I spins.) At temperatures below the TID minimum,
_1-- .1 TID
tc
(1)
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