A constitutive model of temperature gradient driving diffusion in solids with stress effect

In the presence of temperature gradient, the non-uniform redistribution of solute atom usually occurs in an initially uniform solid, e.g. the segregation of alloy element in the gas turbine blade, and this phenomenon is called as Ludwig-Soret effect. The redistribution process of solute atom accompanies a significant stress in solids, which was not taken into account in previous theories. In this paper, in the framework of the irreversible thermodynamics, we establish a constitutive model of temperature gradient driving diffusion. The redistribution process of solute atom and the effect of stress are investigated, respectively. The results reveal that our established model describes the redistribution law of solute atom and clarifies the implied mechanism. And the redistribution of solute atom firstly starts at the hot end and gradually extends towards the cold end. Stress retards the diffusion driven by the temperature gradient and then reduces the non-uniform redistribution of solute atom. Moreover, the obtained quantitative relationship predicts the direction and magnitude of the formed concentration gradient. According to our results, researchers can optimize the distribution of element and evaluate the service performance of engineering materials.