Institute of Metals Division - Calculation of Diffusion Coefficients by the Matano-Boltzmann Method

MUCH information on intermetallic diffusion has been obtained in experiments in which two volumes, initially at different uniform concentrations, are maintained in contact at an interface which is plane, or nearly so. Concentration-distance curves are obtained after suitable times, and analyzed on the basis of a one-dimensional form of Fick's law In early work the linear equation to which Eq. 1 reduces when D is independent of concentration was used. However, when the initial concentrations c, and c, are appreciably different this simplification is often unjustified, and the suggestion by Matanol in 1933 of a way of avoiding it was welcomed. Matano's paper was based on work done as early as 1882 by Boltzmann.2,3 In 1938 Rhines and Meh14 reported an extensive investigation of systems in which the diffusion coefficient depends strongly on concentration, and included a detailed description of the Matano-Boltz-mann method. To a large degree, this description represents the formal method as it is understood and applied today, most later discussions having emphasized thermodynamic and mechanistic aspects of diffusion. Exceptions are the comments of R. V. Churchill, contained in a paper by Ham, Parke and Herzig,5 and the papers by Hall8 and by Kirkaldy.7 More discussion appears necessary since some aspects of the problem remain obscure. Better computational procedures are also needed. The common method, involving graphical determination of slopes and areas, is inconvenient and makes the estimation of errors difficult. Background of the Matano-Boltzmann Method Eq. 1 is to be considered along with initial and boundary conditions. Take the origin of x at the