Determination of diffusion coefficients by measurements of electrical resistivity
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THE electrical resistivity 0 is an attractive tool to study the kinetics of the pick-up and release of a gaseous component by a specimen in an absorption/desorption experiment. A determination of the diffusion coefficient D of this component from the time behavior of the resistivity is relatively easy, provided that its mean concentration X can be inferred from the measured resistivity values. TM The ideal case is when X depends linearly on 0. A preliminary report which describes how this method was used to evaluate the diffusion coefficients of hydrogen and deuterium at very low concentrations in Fe0.sTi0.5has been given. 5 An examination of the literature shows that it was only used in a few other cases, 6-s since the inhomogeneous distribution of the diffusing component which complicates the relationship between the two quantities X and p. The deviation from a linear one depends on the experimental parameters, especially on the total change of the resistivity of the specimen caused by the pick-up or release of the alloying component. The aim of this paper is to provide a rule for the choice of this parameter in such a way that the deviation from linearity is kept at a level which is low enough to permit an easy and accurate determination of D. II. M A T H E M A T I C A L F O R M U L A T I O N We start with a specimen in which component A is dissolved homogeneously at a level X 0. Its resistivity P0 contains a contribution due to X 0, as well as one due to other scattering centers, e.g. lattice vibrations or ternary alloying elements. Only elongated specimens are considered because they have the most suitable shapes for resistivity measurements. Equivalent conditions should exist along the main axis of the specimens and for the ribbons their width should be much larger than their thickness. This leads to an one-dimensional diffusion situation and only one transverse coordinate r is needed to express the spatial dependance of the local concentration x ( r , t ) . At some initial time t = 0 the specimen is coupled under isothermal conditions to a large reservoir containing A. A transfer flow of A takes place until its chemical potentials are equal in both subsystems. This causes the local concentration of A to evolve with time J.-M. W E L T E R is Research Associate and J.-D~ WITT is Senior Technician, Institut fur Festk0rperforschung, K F A JOlich, D-5170 J01ich, W. Germany. Manuscript submitted January 13, 1981.
from its initial value X o to a final one X~, which is fixed by the new thermodynamic equilibrium condition. It is important to realize that this is an adjustable concentration and that it can be varied by changing the conditions which exist in the reservoir, e.g. the pressure when the reservoir is a gaseous atmosphere. The total change of the concentration (X~o - X0) should be small enough to justify the use of a mean value of the diffusion coefficient. The formulae which describe the evolution of x ( r , t ) are given in the next subsection and the mean concentration X (t) is obtained by spatial integr
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