A thermodynamic extremal principle incorporating the constraints from both fluxes and forces. II. Application to isothermal diffusion in multi-principal element alloys

The thermodynamic extremal principle incorporating the constraints from both fluxes and forces proposed in part I was applied to isothermal diffusion in multi-principal element alloys (MPEAs) to propose the so-called double-constraint model. The model cannot reduce physically to the previous model considering only the constraint from fluxes (i.e., the single-constraint model) but in special cases reduces to Fick's law and Darken's equation, showing its reliability. Similar to the previous pair-wise model and single-constraint model, the solutes and solvent do not need to be defined in advance in the double-constraint model and the model can be also applied directly to diffusion in MPEAs. Applications to isothermal diffusion in CoCrFeMnNi pseudo-binary diffusion couple and CoCrFeNi, CoCrFeMnNi body-diagonal diffusion couples showed that the present double-constraint model overall predicted better the experimental results than the previous single-constraint model, indicating again the necessity to consider the constraints from both fluxes and forces in the phenomenological theory of Onsager.