Part I – January 1969 - Communications - Dislocation Pipe Diffusion in Silver Single Crystals

THERE has been interest recently in the conditions under which dislocation pipe diffusion may be observed. In order to extend the measurements to temperatures below Tm/2, where pipe diffusion becomes more important, a chemical sectioning technique was developed for silver single crystals which makes possible the removal of layers of 100A or less. The procedure is briefly as follows. Silver single crystals of 99.995 pct purity were cut in the form of discs t by 4 in., electropolished, and electropolated with Ag110 to about 1000A thickness. The thickness was determined by calibrating the activity with the weight of heavier platings, up to 10,000A. Both diffused and undiffused samples were sectioned in a two-step process. Reaction with a solution of iodine in alcohol formed a thin, even layer of AgI, which was then dissolved in a KCN solution. The reaction rate of the iodine solution varied slightly over a period of time, so that the thickness of the stripped layers, while quite even and regular for a given specimen, ranged from 65 to l00W for different specimens. This variation was checked by using a thickly plated standard with each run. Layer thickness was determined from undiffused samples by the point where the layer activity drops to half the maximum. This maximum intensity also provides, with appropriate corrections, the initial concentration per layer co. Because of the small penetration distances, it is necessary to use the exact solution of Fick's law for a source of finite thickness.' For a plating of thick- where c is the concentration at depth x. flj the error function, D the apparent diffusion coefficient, and t the time. The diffusion coefficient was obtained from the concentration-penetration data by extrapolating to x = 0 where c/co = erf h/2(Dt)1/2 Enough points were taken to impart confidence in the accuracy of the intersection, generally about ten layers. Four temperatures were used as in Table I. For best accuracy, t and h were chosen to give values of the parameter (Dt)1/2/h between 1.0 and 1.7. A typical concentration-penetration curve is shown in Fig. 1. The diffusion coefficients calculated from Eq. [I] are plotted in Fig. 2. For comparison, the high-temperature data of Tomizuka and sonder 2 which go down to 630°C are plotted as the solid line 2(a) from their expression D = 0.40 exp (-44,090/RT). Also for comparison, the lowest temperature point of Hoffman and Tumbull3 is plotted. It is apparent that our data diverge appreciably from the high-temperature extrapolation by 373°C. A better straight line fit for the low-temperature portion is obtained by subtracting the extrapolated volume diffusion coefficient from the apparent. or measured coefficient, and plotting the difference, curve (h) of