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Diffusion |
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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. |
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From:
Ragone, "Thermodynamics of Materials," Wiley (1995) |
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·
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. |
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