Up to now we have assumed that only concentration gradients provide a driving force for diffusion. We now generalize this, by including all forms of free-energy gradient. This will lead us fairly easily to a general theory of diffusion that includes Fick's First Law as a special case. We will apply our new understanding to problems such as diffusion due to an electrical field or a mechanical stress. We will finish the chapter by seeing how this method can help to understand diffusion in multicomponent systems.

Theory

Throughout this book we have considered that diffusional processes are solely driven by concentration gradients. This is based on the concept that a material strives towards equilibrium, and that equilibrium is defined as a state of uniform concentration. In materials science, however, we recognize that this is a rather naive definition of equilibrium. To be more precise, we should state that a body is at equilibrium when the free energy is uniform throughout. Using this definition, we can broaden considerably the range of situations in which diffusion occurs. Thus, we expect diffusion not only in response to concentration gradients, but also due to electrical and thermal fields, and mechanical