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Diffusion
Fixed Surface Mass Situation

· For a fixed mass, M, of A-atoms deposited on the surface of a B -matrix the diffusion profile c(x,t) is:
c(x,t) = {M/(πD(T) t)1/2} exp [- x2/4D(T)t]

· The "length scale" of the process is determined by time and the diffusion temperature through D(T): Length scale ~ (4D(T)t)0.5.

· The graph shows the diffusion profile at constant temperature at three times: t21 > t = 0.

From: Ragone, "Thermodynamics of Materials," Wiley (1995)
· The area under the diffusion profile is constant and equal to the initial mass placed on the surface.
· As the diffusion time tends to infinity, the profile tends to zero at all locations as the same initial mass is distributed over a larger volume.