Since Fick's law cannot be directly integrated for variable , values must be obtained experimentally. An outline is given of the most common method - the Matano analysis. A 'pure' diffusion couple is created and annealed at a constant temperature for a given length of time. After removal from the furnace, a concentration profile is generated. From this, the Matano interface is defined as being the plane across which an equal number of atoms have crossed in both directions.
Some real data is provided in an additional exercise, from which a plot of versus C can be obtained.
The section is completed by 2 graphical simulations of diffusion processes. For simplification, the crystal structure and atomic size of both species are identical. A graph below the atomic array continually updates the 'interpenetration profile'. Furthermore, the initial number of vacancies on each side of the couple may be set. These numbers are used to approximate 'equilibrium vacancy concentrations' on each side of the couple, and these concentrations are automatically maintained at or near 'equilibrium' throughout the simulation.