Chapter 5: Problem 2
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 interdiffusion. Suggest one way in which selfdiffusion may be monitored.
Chapter 5: Problem 2
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 interdiffusion. Suggest one way in which selfdiffusion may be monitored.
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Get started for freeConsider the diffusion of some hypothetical metal Y into another hypothetical metal \(Z\) at \(950^{\circ} \mathrm{C}\); after \(10 \mathrm{~h}\) the concentration at the \(0.5 \mathrm{~mm}\) position (in metal \(Z\) ) is \(2.0 \mathrm{wt} \% \mathrm{Y}\). At what position will the concentration also be \(2.0 \mathrm{wt} \% \mathrm{Y}\) after a \(17.5-\mathrm{h}\) heat treatment again at \(950^{\circ} \mathrm{C}\) ? Assume preexponential and activation energy values of \(4.3 \times 10^{-4} \mathrm{~m}^{2} / \mathrm{s}\) and \(180,000 \mathrm{~J} / \mathrm{mol}\), respectively, for this diffusion system.
The diffusion coefficients for nickel in iron are given at two temperatures, as follows: \begin{tabular}{cc} \hline \(\boldsymbol{T}(\boldsymbol{K})\) & \(\boldsymbol{D}\left(\mathrm{m}^{2} / \mathrm{s}\right)\) \\ \hline 1473 & \(2.2 \times 10^{-15}\) \\ \hline 1673 & \(4.8 \times 10^{-14}\) \\ \hline \end{tabular} (a) Determine the values of \(D_{0}\) and the activation energy \(Q_{d^{\prime}}\) (b) What is the magnitude of \(D\) at \(1300^{\circ} \mathrm{C}(1573 \mathrm{~K}) ?\)
The activation energy for the diffusion of copper in silver is \(193,000 \mathrm{~J} / \mathrm{mol}\). Calculate the diffusion coefficient at \(1200 \mathrm{~K}\left(927^{\circ} \mathrm{C}\right)\), given that \(D\) at \(1000 \mathrm{~K}\left(727^{\circ} \mathrm{C}\right)\) is \(1.0 \times 10^{-14} \mathrm{~m}^{2} / \mathrm{s}\).
Indium atoms are to be diffused into a silicon wafer using both predeposition and drive-in heat treatments; the background concentration of In in this silicon material is known to be \(2 \times 10^{20}\) atoms \(/ \mathrm{m}^{3}\). The drive-in diffusion treatment is to be carried out at \(1175^{\circ} \mathrm{C}\) for a period of \(2.0 \mathrm{~h}\), whichgives a junction depth \(x_{j}\) of \(2.35 \mu \mathrm{m}\). Compute the predeposition diffusion time at \(925^{\circ} \mathrm{C}\) if the surface concentration is maintained at a constant level of \(2.5 \times 10^{26}\) atoms \(/ \mathrm{m}^{3}\). For the diffusion of In in Si. values of \(Q_{d}\) and \(D_{0}\) are \(3.63 \mathrm{eV} /\) atom and \(7.85 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s}\), respectively.
Carbon is allowed to diffuse through a steel plate 10 -mm thick. The concentrations of carbon at the two faces are \(0.85\) and \(0.40 \mathrm{~kg} \mathrm{C} / \mathrm{cm}^{3} \mathrm{Fe}\), which are maintained constant. If the preexponential and activation energy are \(5.0 \times 10^{-7} \mathrm{~m}^{2} / \mathrm{s}\) and 77,000 \(\mathrm{J} / \mathrm{mol}\), respectively, compute the temperature at which the diffusion flux is \(6.3 \times 10^{-10} \mathrm{~kg} / \mathrm{m}^{2} \mathrm{~s}\).
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