Introduction to Diffusion - Department of Materials Science and ...

Carea undereach curve isconstantx∞Fig. 3: Exponential solution. Note how the curvaturechanges with time.functions obtained above, each slightly displaced along the x axis, andsumming (integrating) up their individual effects. The integral is in factthe error functionerf{x} = 2 √ π∫ xso the solution to the diffusion equation is0exp{−u 2 }duboundary conditions:C{x = 0, t} = C sand C{x, t = 0} = C 0{ } xC{x, t} = C s − (C s − C 0 )erf2 √ DtThis solution can be used in many circumstances where the surfaceconcentration is maintained constant, for example in the carburisationor decarburisation processes (the concentration profiles would be thesame as in Fig. 4, but with only one half of the couple illustrated). Thesolutions described here apply also to the diffusion of heat.Mechanism of DiffusionAtoms in the solid–state migrate by jumping into vacancies (Fig. 5).The vacancies may be interstitial or in substitutional sites. There is,