“…In the empirical description of transport by thermal diffusion, because of the complexity of this process when the temperature gradient (▽ T ) creates an additional driving force to the concentration gradients (▽ C ), the Ludwig–Soret effect can be taken into account. In this case, the formulae can be used to express the flux linking to thermal diffusion: i.e., two temperature gradient‐driven phenomena can be outlined: - D ▽ C – flux of depositing and diffusing atoms caused by their non‐uniform spatially distributed concentration due to temperature spatial non‐uniformity;
- DC ( Q/kT )(▽ T/T ) – clear expression of the Ludwig–Soret effect in crystalline solids.
where D ( C , T , t ) is the diffusivity, s ( T , t ) is the solubility, k s ( C , T , t ) is the “Soret effect” factor providing diffusion because of temperature gradient, and k p ( c , T , t ) is the pressure stress factor. The temperature gradient can be created at thermal treatment resulting in the independent driving force for the concentration gradient.…”