Chapter 5: Problem 3
(a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.
Chapter 5: Problem 3
(a) Compare interstitial and vacancy atomic mechanisms for diffusion. (b) Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.
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Get started for freeAn FCC iron-carbon alloy initially containing 0.10 wt \(\% \mathrm{C}\) is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at 1.10 wt\%. If after 48 h the concentration of carbon is \(0.30 \mathrm{wt} \%\) at a position \(3.5 \mathrm{mm}\) below the surface, determine the temperature at which the treatment was carried out.
The purification of hydrogen gas by diffusion through a palladium sheet was discussed in Section \(5.3 .\) Compute the number of kilograms of hydrogen that pass per hour through a 6 -mm-thick sheet of palladium having an area of \(0.25 \mathrm{m}^{2}\) at \(600^{\circ} \mathrm{C}\). Assume a diffusion coefficient of \(1.7 \times 10^{-8} \mathrm{m}^{2} / \mathrm{s},\) that the concentrations at the high- and low-pressure sides of the plate are 2.0 and \(0.4 \mathrm{kg}\) of hydrogen per cubic meter of palladium, and that steady-state conditions have been attained.
Consider a diffusion couple composed of two semi-infinite solids of the same metal, and that each side of the diffusion couple has a different concentration of the same elemental impurity; furthermore, assume each impurity level is constant throughout its side of the diffusion couple. For this situation, the solution to Fick's second law (assuming that the diffusion coefficient for the impurity is independent of concentration), is as follows: $$C_{x}=\left(\frac{C_{1}+C_{2}}{2}\right)-\left(\frac{C_{1}-C_{2}}{2}\right) \operatorname{erf}\left(\frac{x}{2 \sqrt{D t}}\right).$$In this expression, when the \(x=0\) position is taken as the initial diffusion couple interface, then \(C_{1}\) is the impurity concentration for \(x<0\) likewise, \(C_{2}\) is the impurity content for \(x>0\).A diffusion couple composed of two platinum-gold alloys is formed; these alloys have compositions of \(99.0 \mathrm{wt} \% \mathrm{Pt}-1.0 \mathrm{wt} \%\) Au and 96.0 wt \(\%\) Pt- 4.0 wt\% Au. Determine the time this diffusion couple must be heated at \(1000^{\circ} \mathrm{C}(1273 \mathrm{K})\) in order for the composition to be 2.8 wt \(\%\) Au at the \(10 \mu \mathrm{m}\) position into the \(4.0 \mathrm{wt} \%\) Au side of the diffusion couple. Preexponential and activation energy values for Au diffusion in \(\mathrm{Pt}\) are \(1.3 \times 10^{-5}\) \(\mathrm{m}^{2} / \mathrm{s}\) and \(252,000 \mathrm{J} / \mathrm{mol},\) respectively.
Nitrogen from a gaseous phase is to be diffused into pure iron at \(675^{\circ} \mathrm{C}\). If the surface concentration is maintained at \(0.2 \mathrm{wt} \% \mathrm{N}\) what will be the concentration \(2 \mathrm{mm}\) from the surface after 25 h? The diffusion coefficient for nitrogen in iron at \(675^{\circ} \mathrm{C}\) is \(1.9 \times 10^{-11} \mathrm{m}^{2} / \mathrm{s}\).
Self-diffusion involves the motion of atoms that are all of the same type; therefore it is not subject to observation by compositional changes, as with inter-diffusion. Suggest one way in which self-diffusion may be monitored.
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