- Fick's first law: J = -D grad c. This is an empirical law and it is consistent with the theory of linear irreversible thermodynamics.
- Fick's second law: dc / dt = - grad J. This is a consequence of the conservation of matter. Note that if the diffusivity varies with c, the resulting differential equation is nonlinear.
The Law of Conservation of Matter states that matter cannot be created or destroyed, only redistributed. In chemistry, it is represented by the fact that the sum of the masses of the reactants are equal to the sum of the products formed in a chemical reaction.
In heat transfer analysis, thermal diffusivity (symbol: α) is the ratio of thermal conductivity to volumetric heat capacity.
In mathematics, a differential equation is an equation which involves the derivatives of an unknown function represented by a dependent variable.
- The equations of heat conduction are of identical form to Fick's laws: JQ = - k grad T and dT/dt = -grad JQ.
- Self-diffusion in a chemical pure material can be measured by using radioisotope that is easily tracked. The application of force-flux equations for the two isotopes yields a Fick's law-type expression for the radiotracer, KoM Eq. 3.4.
A radionuclide is an atom with an unstable nucleus. The radionuclide undergoes radioactive decay by emitting a gamma ray(s) and/or subatomic particles. Radionuclides may occur naturally, but can also be artificially produced.
Radionuclides are often referred to by chemists and biologists as radioactive isotopes or radioisotopes, and play an important part in the technologies that provide us with food, water and good health. However, they can also constitute real or perceived dangers.
- Self-diffusion in a homogeneous alloy (uniform composition) can also be measured by using a radioisotope of one of the species. The application of force-flux equations for the various species present yields a Fick's law-type expression for the radiotracer, KoM Eq. 3.5.
- Self-diffusion in crystalline materials and in many alloy crystals occurs by the vacancy mechanism.
In crystallography, a vacancy is a point defect in a crystal. Crystals inherently possess imperfections, often referred to as 'crystalline defects'. A defect wherein an atom, such as silicon, is missing from one of the sites is known as a 'vacancy' defect.
- Interdiffusion occurs in an alloy with composition gradients. The motion of each species in a reference frame fixed to the crystal follows Fick's first law, with a proportionality constant known as the intrinsic diffusivity. The intrinsic diffusivities and the self-diffusivities are related by KoM Eq. 3.13 and the relation involves a thermodynamic factor. Nonideality can either accelerate or retard interdiffusion kinetics, relative to kinetics measured in the absence of a chemical gradient.
- During interdiffusion the intrinsic diffusivities are not necessarily equal. This gives rise to a set of phenomena known as the Kirkendall effect. The interdiffusion can be described as "volume-fixed" (laboratory) reference frame by a single diffusion coefficient known as the interdiffusivity which is related to the intrinsic diffusivities by the Darken equation.
- Consider describing diffusion of a drop of ink into water from a boat moving in a river. If you describe the diffusion from the moving reference frame of the boat it is like the C-frame (i.e., viewing atoms whizzing by a specific plane of atoms in the crystal). If you describe diffusivities from the fiver frame, it is like the V-frame. In an alloy crystal with unequal intrinsic diffusivities the net flow of mass (analogous to the river current) arises from the net flux of vacancies that results in apparent "motion" of the crystal planes in the interdiffusion zone relative to the ends of the sample.