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Diffusion
Surface Hardening

· The carbon content of the surface is controlled by selecting a diffusion temperature and time: {c(x,t)T - c0}= {cs- c0}[ 1 - erf(x/ {4Dt}0.5)]
where D = D0exp(-Q/kT)
· The maximum penetration depth corresponds to an error function argument of 2: erf(2) = 0.995; [1 - erf(2)] = 0; c(x,t)T = c0
· Penetration Depth = 2(4Dt)0.5 = 4(Dt)0.5

From: Guy & Hren, "Elements of Physical Metallurgy," Addison Wesley (1974)