Modelling Considerations for the Effect of Temperature Gradients on Redistribution of Hydrogen in Zirconium

Abstract Diffusion of hydrogen in Zirconium is known to be subject to the Soret effect whereby temperature gradients contribute to the usual Fick’s law driving force. The Soret effect is quantified by the heat of transport, Q*, for which positive values result in movement of hydrogen from hot to cold regions. Typically, Fick’s law along with the Soret effect is applied only to the portion of hydrogen that is in solid solution; complications may arise when hydrogen concentration in excess of the solubility limit is in the form of hydride. Some experiments have shown results that are not explained by models that restrict hydrogen transport to the solute part. To address these findings, models have been proposed to account for the two-phase nature of the system when hydrogen concentration exceeds solid solubility. The models introduce an additional Q* value such that particular experimental observations can be better predicted, but the mechanics of each method differ to the extent that the proposed Q* values agree neither in sign nor magnitude. Whenever hydrides are present, characterization of the terminal solid solubility (TSS) becomes an important part of the overall diffusion model. Recent advances have quantified transient effects of dissolution and precipitation of hydrides, and these transient effects can affect the net mobility of hydrogen. The objective of this work is to simulate experiments to examine how the solubility model in the presence of a temperature gradient can affect the transient response leading to the experimentally determined distributions. Comparison is made for time-independent TSS and the transient HNGD (Hydride Nucleation Growth Dissolution) model published for Zircaloy. Also, additional consideration is given to longer time behavior not directly addressed in the HNGD model. The results of the study show how different features in the TSS model affect the predicted redistribution. Use of a more representative TSS model can reasonably predict experimental results without introducing additional hydride diffusion parameters.