A Numerical Calculation of the Redistribution of an Interstitial Solute in a Thermal Gradient

An analytical method is described which enables one to calculate the concentration profile of an interstitial solute of finite solubility in an alloy under a given thermal gradient. The method requires that one know beforehand the diffusion coefficient, the terminal solid solubility, and the heat of transport of the solute. The work is applied to the experimental conditions of Sawatzky and of Markowitz for hydrogen in Zircaloy. The agreement between the predicted profiles and the experimentally determined profiles is quite good for total concentrations less than ∼1000 ppm. For concentrations greater than this, some deviation is seen but the overall agreement is still considered good within the accuracy of the assumptions employed. The principles embodied in the analysis are easily generalized to include multidimensional thermal and concentration gradients.