Elimination of Systematic Error in Diffusion Measurement Using In-situ X-ray Fluorescence Analysis for Liquid Alloys

The objective of the present study is to quantify and eliminate the error factors in the measurement of diffusion coefficients in liquid alloys by using in-situ X-ray fluorescence analysis (in-situ XRF). Averaging effect, initial mass transport, and matrix effect were investigated. The impurity diffusion coefficient of Bi in liquid Sn was measured at 573 K using a combination of the long capillary technique and in-situ XRF. The apparent diffusion coefficient was obtained as the time -series data by fitting an analytical solution of Fick's second law to the temporal variation in Bi concentration in the capillary. In the present measurement, matrix effect did not induce a significant error in the measured diffusion coefficient. Averaging effect can be eliminated by convoluting the analytical solution with the distribution of the X-ray fluorescence intensity scanned from the rod sample. Furthermore, the initial mass transport can be eliminated by shifting the point of time origin to the latter time in the temporal variation in the measured concentration by fitting the analytical solution. By performing the above corrections, the systematic error in the measured diffusion coefficient can be reduced.