Part II – February 1969 - Papers - Effects of Short-Circuiting Paths on Diffusion Coefficient Measurements

Effects of short-circuiting paths on observed diffusion behavior in real crystalline systems are considered. It is concluded that experimentally measured diffusion coefficients may vary widely from values associated with true lattice diffusion to those appropriate for short-circuiting paths alone depending upon the conditions of the experiment and the sensitivity and completeness of the data. IN 1961 Harrison1 classified experimentally observed diffusion behavior in systems involving both lattice and dislocation-enhanced atomic transport into three categories. His types A and C were limiting cases where the measured diffusion coefficients using the usual serial sectioning techniques were representative of lattice diffusion (with only slight effects of dislocations) and dislocation-network diffusion (with only slight effects from lattice diffusion), respectively. In both cases A and C for a sectioning experiment in which the diffusion couple has the semi-infinite geometry and unidirectional diffusion takes place from a plane source located at the origin of the coordinate system, he pointed out that Gaussian penetration behavior should be observed. For case A the lattice coefficient should be slightly enhanced by dislocation contributions, and the model of Hart2 can be used to predict the amount of this enhancement. For case C the observed coefficient should be that for the dislocation network and have little or nothing to do with lattice diffusion. Hart's model in its general form is still applicable, but the apparent diffusion coefficient for this case is virtually independent of dislocation density. Harrison's case B is that for which non-negligible contributions exist for transport by both mechanisms and "the concentration distribution does not approximate to any simple form." With the possible exception of very low temperatures where diffusion distances approach atomic dimensions, any real diffusion specimen will in general show non-Gaussian behavior provided the data are complete enough to uncover it. Thus, a "complete" set of data for any real system cannot be expected to be totally amenable to treatment by a simple mathematical model which does not take into account the relative distribution of transport by the various modes or submodes. For a particular sensitivity of specimen analysis and at a given temperature of annealing if the concentration profile could be observed as a function of time, "the behavior will initially be type C, and will develop into type B. and ultimately type A".1 Thus, it appears that the type of diffusion behavior which is experimentally observed in a given system depends very much upon the particular experimental conditions and the particular tools available to obtain the data. Interpreted in this fashion, Harrison's classification refers not to the diffusion behavior as a whole but to the relative sensitivity of the method of examination and completeness of the data. In the present paper we will: 1) assume that the measured penetration behavior follows the same general classification as that proposed by Harrison; 2) give, for diffusion in tungsten, examples of the range of diffusion coefficients that it is possible to obtain in a single experiment; and 3) speculate that some arguments which consider the possibility of short-circuiting effects being responsible for "anomalous" diffusion in several bcc metals may have been discarded prematurely.3 Both monocrystalline and polycrystalline tungsten were used in this work. The former was obtained as triple-pass, electron-beam zone-refined 6.0-mm-diam rod from Materials Research Corp.. Orange-burg. N.Y. The latter was swaged, high-purity bar stock which was annealed for 2 hr at 2200°C and 10-9 torr to yield an average grain diameter of about 25 /i. The tracer Nb95 was received in oxalate solution from the Isotopes Division, Oak Ridge National Laboratory. Experimental procedures of specimen preparation, isothermal diffusion annealing, serial sectioning by anodizing-and-stripping, and y counting of the individual sections to determine the tracer penetration profile after a given diffusion anneal have been described elsewhere.4 However, it should be noted that the anodizing-stripping sectioning technique has the particular advantage for this research of permitting sectioning to be accomplished over a wide range of