Uncertainty Analysis of Ternary Diffusivities Obtained from One Versus Two Compact Diffusion Couples

Abstract

An uncertainty analysis is given for how the measurement uncertainty of concentration profiles propagates into calculated ternary diffusivity or square-root diffusivity coefficients. The analysis is performed on analytical equations for calculating square-root diffusivities from one and two-diffusion couples. The equations assume that the concentration differences in the couples are so compact that their concentration profiles fit the error function solution to the diffusion equation. In other words the equations assume constant diffusivity. An example is given that illustrates how the relative uncertainty of each square-root diffusivity coefficient varies with composition vector orientation. The major conclusion is that diffusivities calculated from two-diffusion couples are reliable and have predictable uncertainty that parallels experimental uncertainty. The uncertainty is predictable by inserting the measured diffusivity into the equations given in this paper. However coefficients in ternary diffusivities calculated from one-diffusion couple may contain uncertainty that is unbounded. Therefore they are not reliable unless additional information is known about the diffusivity. However one exceptional case is noted. As reported before using a different analysis, errors in coefficients from one column of the square-root diffusivity matrix are the same for one and two-diffusion couple experiments when the one couple method is performed on a compact, quasi-binary couple.