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Diffusion
Fixed Surface Concentration Case

· For a fixed surface concentration of A-atoms diffusing into an B-matrix at a constant temperature T: 
(c(x,t) - c0) = (cs - c0){1 - erf(x/ [4Dt]0.5)}
where erf(y) = (2/π1/2) 0 ¤ y exp(-z2) dz ; the Gaussian Error Function, and c0 is the initial concentration of A in the B-matrix.
From: Ragone, "Thermodynamics of Materials," Wiley (1995)
· For small values of its argument, the value of the error function is approximately equal to the argument.
· When the argument is 2, the value of the error function is 0.995, and the increased concentration c(x, t) goes to zero. This can be used to estimate the time for a given diffusion depth.