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 freeThe preexponential and activation energy for the diffusion of iron in cobalt are \(1.1 \times 10^{-5}\) \(\mathrm{m}^{2} / \mathrm{s}\) and \(253,300 \mathrm{~J} / \mathrm{mol}\), respectively. At what temperature will the diffusion coefficient have a value of \(2.1 \times 10^{-14} \mathrm{~m}^{2} / \mathrm{s}\) ?
The diffusion coefficients for silver in copper are given at two temperatures: $$ \begin{array}{cc} \hline T\left({ }^{\circ} \mathrm{C}\right) & D\left(\mathrm{~m}^{2} / \mathrm{s}\right) \\ \hline 650 & 5.5 \times 10^{-16} \\ 900 & 1.3 \times 10^{-13} \\ \hline \end{array} $$ (a) Determine the values of \(D_{0}\) and \(Q_{d}\). (b) What is the magnitude of \(D\) at \(875^{\circ} \mathrm{C}\) ?
At approximately what temperature would a specimen of \(\gamma\)-iron have to be carburized for \(2 \mathrm{~h}\) to produce the same diffusion result as at \(900^{\circ} \mathrm{C}\) for \(15 \mathrm{~h}\) ?
Phosphorus atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of \(\mathrm{P}\) in this silicon material is known to be \(5 \times 10^{19}\) atoms \(/ \mathrm{m}^{3}\). The predeposition treatment is to be conducted at \(950^{\circ} \mathrm{C}\). for 45 minutes; the surface concentration of \(P\) is to be maintained at a constant level of \(1.5 \times 10^{26}\) atoms \(/ \mathrm{m}^{3}\). Drive-in diffusion will be carried out at \(1200^{\circ} \mathrm{C}\) for a period of \(2.5 \mathrm{~h}\). For the diffusion of \(\mathrm{P}\) in \(\mathrm{Si}\), values of \(Q_{d}\) and \(D_{0}\) are \(3.40 \mathrm{eV} /\) atom and \(1.1 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s}\), respectively. (a) Calculate the value of \(Q_{0}\). (b) Determine the value of \(x_{j}\) for the drive-in diffusion treatment. (c) Also for the drive-in treatment, compute the position \(x\) at which the concentration of \(P\) atoms is \(10^{24} \mathrm{~m}^{-3}\).
A sheet of steel \(1.5 \mathrm{~mm}\) thick has nitrogen atmospheres on both sides at \(1200^{\circ} \mathrm{C}\) and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is \(6 \times 10^{-11} \mathrm{~m}^{2} / \mathrm{s}\), and the diffusion flux is found to be \(1.2 \times\) \(10^{-7} \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{s}\). Also, it is known that the concentration of nitrogen in the steel at the highpressure surface is \(4 \mathrm{~kg} / \mathrm{m}^{3} .\) How far into the sheet from this high-pressure side will the concentration be \(2.0 \mathrm{~kg} / \mathrm{m}^{3}\) ? Assume a linear concentration profile.
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